UOR Interaction Algebra

IRI: https://uor.foundation/interaction/
Prefix: interaction:
Space: bridge
Comment: Multi-entity interaction: commutator states, associator triples, negotiation convergence.

This is a bridge-space namespace in the Resolve stage of the PRISM pipeline. It provides the resolution infrastructure — queries, partitions, observables, proofs, derivations, and traces that transform inputs into certified results.

Learn more: Pipeline Overview

Class hierarchy

Imports

https://uor.foundation/op/
https://uor.foundation/convergence/
https://uor.foundation/state/
https://uor.foundation/observable/
https://uor.foundation/schema/

Classes

Name	Subclass Of	Comment
`InteractionContext`	`Thing`	Two entities sharing sites through composed operations. Properties: entityA, entityB, sharedSiteMask, commutatorNorm.
`CommutatorState`	`Thing`	The norm ‖[δ_A, ι_B]‖ on shared sites. Zero iff operators commute on the shared domain.
`AssociatorState`	`Thing`	The norm of the three-way associator on shared sites.
`AssociatorTriple`	`Thing`	Three entities whose interaction exhibits non-associativity due to read-write interleaving.
`ThreeWaySite`	`Thing`	A site shared by all three entities in an AssociatorTriple.
`NegotiationTrace`	`Thing`	Sequence of CommutatorStates across interaction steps.
`MutualModelTrace`	`Thing`	Sequence of AssociatorStates across interaction steps.
`InteractionNerve`	`Thing`	Simplicial complex of N-entity coupling.
`InteractionComposition`	`Thing`	IC(A,B) = κ(session(A,B)). Combined interaction-composition operator.

Properties

Name	Kind	Functional	Domain	Range	Comment
`entityA`	Object	true	`InteractionContext`	`TermExpression`	First entity in the interaction context.
`entityB`	Object	true	`InteractionContext`	`TermExpression`	Second entity in the interaction context.
`sharedSiteMask`	Datatype	true	`InteractionContext`	`nonNegativeInteger`	Bitmask identifying which sites are shared between the two entities.
`commutatorNorm`	Datatype	true	`InteractionContext`	`decimal`	The norm of the commutator on shared sites. Zero iff the operators commute.
`commutatorValue`	Datatype	true	`CommutatorState`	`decimal`	The computed commutator norm value.
`associatorNorm`	Datatype	true	`AssociatorState`	`decimal`	The norm of the three-way associator on shared sites.
`tripleComponentA`	Object	true	`AssociatorTriple`	`Datum`	First component datum in the associator triple.
`tripleComponentB`	Object	true	`AssociatorTriple`	`Datum`	Second component datum in the associator triple.
`tripleComponentC`	Object	true	`AssociatorTriple`	`Datum`	Third component datum in the associator triple.
`sitePosition`	Datatype	true	`ThreeWaySite`	`nonNegativeInteger`	The position index of the shared site.
`leftGroupingValue`	Datatype	true	`ThreeWaySite`	`decimal`	Value under left-associative grouping (AB)C.
`rightGroupingValue`	Datatype	true	`ThreeWaySite`	`decimal`	Value under right-associative grouping A(BC).
`isPinned`	Datatype	true	`ThreeWaySite`	`boolean`	Whether this site is pinned by a lease constraint.
`pinningPair`	Object	true	`ThreeWaySite`	`TermExpression`	Identifier of the entity pair that pins this site.
`negotiationSteps`	Datatype	true	`NegotiationTrace`	`nonNegativeInteger`	Number of steps in the negotiation trace.
`isConvergent`	Datatype	true	`NegotiationTrace`	`boolean`	Whether the trace converges to zero commutator or zero associator.
`modelConvergent`	Datatype	true	`MutualModelTrace`	`boolean`	Whether the mutual model trace converges.
`nerveDimension`	Datatype	true	`InteractionNerve`	`nonNegativeInteger`	Maximum dimension of the interaction nerve simplicial complex.
`nerveBettiNumbers`	Datatype	true	`InteractionNerve`	`nonNegativeInteger`	Betti number sequence of the interaction nerve.
`reificationDepth`	Datatype	true	`InteractionComposition`	`nonNegativeInteger`	Depth of the interaction composition reification.
`traceLength`	Datatype	true	`NegotiationTrace`	`nonNegativeInteger`	The number of steps in a negotiation trace.
`convergenceRate`	Datatype	true	`NegotiationTrace`	`decimal`	The rate at which the negotiation trace converges.
`terminalValue`	Object	true	`NegotiationTrace`	`TermExpression`	The terminal value of the negotiation trace.
`associatorProfileRef`	Object	true	`AssociatorTriple`	`Observable`	Reference to the observable describing the associativity profile.
`associatorNormValue`	Datatype	true	`AssociatorTriple`	`decimal`	The maximum norm of the associator for this triple.