UOR Resolvers

IRI: https://uor.foundation/resolver/
Prefix: resolver:
Space: bridge
Comment: Type resolution strategies implementing the partition map Π : T_n → Part(R_n). Resolvers transform type declarations into ring partitions.

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 · Resolution & Queries

Class hierarchy

Imports

https://uor.foundation/schema/
https://uor.foundation/query/
https://uor.foundation/partition/
https://uor.foundation/type/
https://uor.foundation/predicate/

Classes

Name	Subclass Of	Disjoint With	Comment
`Resolver`	`Thing`	`ResolutionState`, `RefinementSuggestion`	A strategy for resolving a type declaration into a partition of the ring. The kernel dispatches to a specific resolver based on the type's structure.
`DihedralFactorizationResolver`	`Resolver`		Resolves types by factoring the ring under dihedral group action. Identifies orbits under D_{2^n} to determine irreducibility boundaries.
`CanonicalFormResolver`	`Resolver`		Resolves types by computing canonical forms via term rewriting. Applies the critical identity and normalization rules to reduce terms to unique canonical representatives.
`EvaluationResolver`	`Resolver`		Resolves types by direct evaluation: applies operations to enumerate ring elements and classify them as irreducible, reducible, unit, or exterior.
`ResolutionState`	`Thing`	`Resolver`, `RefinementSuggestion`	The current state of an iterative resolution: tracks how many iterations have been performed, whether the resolution is complete, and the current site deficit.
`RefinementSuggestion`	`Thing`	`Resolver`, `ResolutionState`	A suggestion from the resolver for how to refine an incomplete resolution: which metric axis to explore, which class to narrow to, and which sites to target.
`ComplexityClass`	`Thing`		A computational complexity classification for resolvers. Each resolver's asymptotic runtime is typed as a named ComplexityClass individual rather than a free string.
`CechNerve`	`Thing`, `SimplicialComplex`, `KanComplex`		The simplicial complex whose vertices are constraints and where a k-simplex exists iff the corresponding k+1 constraints have nonempty intersection. The nerve's topology governs resolution convergence: trivial homology ↔ smooth convergence, non-trivial homology ↔ potential stalls.
`CompletenessResolver`	`Resolver`		A specialisation of Resolver driving the completeness certification loop. Accepts a CompletenessCandidate, runs the ψ-pipeline (reading nerveEulerCharacteristic from ResolutionState), and either issues a CompletenessCertificate or produces a RefinementSuggestion.
`WittLevelResolver`	`Resolver`		A Resolver parameterised by quantum level. The same resolver strategy runs at any quantum level n ≥ 1 by substituting the appropriate R_n ring.
`SessionResolver`	`Resolver`		A Resolver that maintains a BindingAccumulator across multiple RelationQuery evaluations. The top-level resolver for multi-turn Prism deployments.
`TypeSynthesisResolver`	`Resolver`		A Resolver that runs the ψ-pipeline in inverse mode. Accepts a TypeSynthesisGoal and returns a TypeSynthesisResult. Internally maintains a ConstraintSearchState tracking which constraint combinations have been explored and which Betti profiles they realise.
`ConstraintSearchState`	`Thing`		Internal resolver state tracking the boundary of explored constraint combinations during synthesis. Carries exploredCount, currentCandidate, and a link to the best SynthesisSignature achieved so far.
`IncrementalCompletenessResolver`	`Resolver`		A Resolver that determines whether a CompleteType T at Q_n lifts to a CompleteType at Q_{n+1} without re-running the full ψ-pipeline from scratch. It computes the SpectralSequencePage sequence, reads the LiftObstruction, and either confirms the lift or returns a LiftRefinementSuggestion.
`LiftRefinementSuggestion`	`RefinementSuggestion`		A RefinementSuggestion produced when a WittLift has a non-trivial LiftObstruction. Specialises RefinementSuggestion with liftSitePosition (the new bit position n+1) and obstructionClass.
`MonodromyResolver`	`Resolver`		A Resolver that computes the HolonomyGroup of a ConstrainedType by enumerating closed paths in the constraint nerve and accumulating DihedralElement values. Outputs a MonodromyClass and classifies the type as FlatType or TwistedType.
`JacobianGuidedResolver`	`Resolver`		A resolver that uses the Jacobian matrix to guide constraint selection, implementing DC_10: select the constraint that maximises total curvature reduction.
`SuperpositionResolver`	`Resolver`		A resolver that handles superposed site states, computing amplitudes and determining when superposition collapses to a classical site assignment (Amendment 32).
`GroundingAwareResolver`	`Resolver`		A resolver that exploits accumulated session bindings at full saturation (σ = 1) to provide O(1) resolution via direct coordinate reads (SC_5).
`GeodesicValidator`	`Resolver`		A resolver that validates whether a ComputationTrace satisfies the dual geodesic condition (AR_1-ordered and DC_10-selected). Produces GeodesicViolation individuals on failure.
`MeasurementResolver`	`Resolver`		A resolver that handles projective collapse of SuperposedSiteState components. Issues MeasurementCertificate upon successful collapse with QM_1 verification.
`TowerCompletenessResolver`	`Resolver`		A Resolver that constructs a LiftChain from liftSourceLevel to an arbitrary liftTargetLevel Q_k by iterating IncrementalCompletenessResolver step by step.
`ExecutionPolicy`	`Thing`	`Resolver`, `ResolutionState`, `RefinementSuggestion`	A strategy class that defines how a SessionResolver orders pending RelationQuery instances for dispatch. The policy reads the targetSite.freeRank of each pending query and applies an ordering function.
`ExecutionPolicyKind`	`Thing`		A typed controlled vocabulary for ExecutionPolicy individuals. Follows the SessionBoundaryType pattern: a single class with named individuals rather than a subclass hierarchy.
`HomotopyResolver`	`Resolver`		A resolver that runs the extended ψ-pipeline (ψ_7–ψ_9) to compute the full homotopy type of a CechNerve. Returns HomotopyGroup observables and PostnikovTruncation records.
`ModuliResolver`	`Resolver`		A resolver that computes the local structure of the moduli space at a given CompleteType: constructs the DeformationComplex, determines the HolonomyStratum, and computes tangent/obstruction dimensions.

Properties

Name	Kind	Functional	Domain	Range	Comment
`inputType`	Object	true	`Resolver`	`TypeDefinition`	The type of input this resolver accepts.
`outputType`	Object	true	`Resolver`	`Partition`	The type of output this resolver produces. For all UOR resolvers, the output is a partition:Partition.
`strategy`	Object	true	`Resolver`	`TermExpression`	A human-readable description of the resolution strategy this resolver implements.
`resolutionState`	Object	true	`Resolver`	`ResolutionState`	The current resolution state of this resolver.
`isComplete`	Datatype	true	`ResolutionState`	`boolean`	Whether this resolution is complete: all sites are pinned and the partition is fully determined.
`iterationCount`	Datatype	true	`ResolutionState`	`nonNegativeInteger`	The number of refinement iterations performed so far.
`siteDeficit`	Object	true	`ResolutionState`	`FreeRank`	The site budget showing the remaining unpinned sites. When all sites are pinned, the deficit is zero and resolution is complete.
`suggestion`	Object	false	`ResolutionState`	`RefinementSuggestion`	A refinement suggestion for advancing this resolution.
`suggestedAxis`	Object	true	`RefinementSuggestion`	`MetricAxis`	The metric axis this suggestion recommends exploring.
`suggestedClass`	Object	true	`RefinementSuggestion`	`Class`	The constraint class this suggestion recommends applying.
`targetSites`	Object	false	`RefinementSuggestion`	`SiteIndex`	The site coordinates this suggestion targets for pinning.
`convergenceRate`	Datatype	true	`ResolutionState`	`decimal`	The rate at which sites are being pinned per iteration. A higher rate indicates faster convergence toward a complete resolution.
`hasComplexityClass`	Object	true	`Resolver`	`ComplexityClass`	The computational complexity class of this resolver. Replaces the string-valued resolver:complexity property.
`cechNerve`	Object	true	`ResolutionState`	`CechNerve`	The constraint nerve associated with this resolution state.
`residualEntropy`	Datatype	true	`ResolutionState`	`decimal`	The residual Shannon entropy of the resolution state: S = freeRank × ln 2. Measures remaining uncertainty.
`topologicallyComplete`	Datatype	true	`ResolutionState`	`boolean`	Whether all Betti numbers of the constraint nerve are zero, indicating no topological obstructions to resolution.
`nerveEulerCharacteristic`	Datatype	true	`ResolutionState`	`integer`	The Euler characteristic χ(N(C)) of the active constraint nerve at this resolution state. IT_7d requires this value to equal n (the quantum level) for resolution to be complete. Cached here to avoid recomputing the full ψ pipeline on each iteration check.
`completenessTarget`	Object	true	`CompletenessResolver`	`CompletenessCandidate`	The CompletenessCandidate this resolver is certifying.
`quantumLevel`	Object	true	`WittLevelResolver`	`WittLevel`	The quantum level this resolver instance is configured for.
`sessionAccumulator`	Object	true	`SessionResolver`	`BindingAccumulator`	The BindingAccumulator this session resolver maintains across multiple RelationQuery evaluations.
`synthesisGoal`	Object	true	`TypeSynthesisResolver`	`TypeSynthesisGoal`	The goal this type synthesis resolver is working to achieve.
`exploredCount`	Datatype	true	`ConstraintSearchState`	`nonNegativeInteger`	Number of constraint combinations evaluated so far during synthesis.
`currentCandidate`	Object	true	`ConstraintSearchState`	`ConstrainedType`	The type candidate currently being evaluated during synthesis.
`liftTarget`	Object	true	`IncrementalCompletenessResolver`	`WittLift`	The WittLift this incremental completeness resolver is evaluating.
`liftSitePosition`	Object	true	`LiftRefinementSuggestion`	`SiteIndex`	The new site position at Q_{n+1} that the lift refinement suggestion targets.
`obstructionClass`	Object	true	`LiftRefinementSuggestion`	`LiftObstructionClass`	The obstruction class this lift refinement suggestion is designed to kill.
`monodromyTarget`	Object	true	`MonodromyResolver`	`ConstrainedType`	The type whose holonomy this monodromy resolver is computing.
`holonomyResult`	Object	true	`MonodromyResolver`	`HolonomyGroup`	The HolonomyGroup produced by this monodromy resolver run.
`guidingJacobian`	Object	true	`ResolutionState`	`Jacobian`	The Jacobian observable guiding constraint selection at this resolution state (DC_10).
`usedGrounding`	Datatype	true	`GroundingAwareResolver`	`boolean`	Whether this resolver used the saturation shortcut (SC_5) to bypass the ψ-pipeline and return a direct coordinate read.
`validateGeodesic`	Object	true	`GeodesicValidator`	`GeodesicTrace`	The GeodesicTrace being validated by this GeodesicValidator.
`collapseAmplitude`	Datatype	true	`MeasurementResolver`	`decimal`	The amplitude of the SuperposedSiteState prior to projective collapse by this MeasurementResolver.
`collapsedSite`	Datatype	true	`MeasurementResolver`	`nonNegativeInteger`	The site index that was collapsed (pinned to a classical value) by the projective measurement.
`measurementOutcome`	Datatype	true	`MeasurementResolver`	`nonNegativeInteger`	The classical value obtained from the projective collapse. Either 0 or 1 for a single-site measurement.
`amplitudeVector`	Datatype	true	`SuperpositionResolver`	`decimal`	The amplitude vector of all branches maintained by this SuperpositionResolver during ψ-pipeline traversal. Encoded as a comma-separated list of decimal amplitudes. Must satisfy Σ\|αᵢ\|² = 1 (QM_5) after normalization.
`priorAmplitudeVector`	Datatype	true	`MeasurementResolver`	`decimal`	The full vector of all branch amplitudes before projective collapse. Recorded by the MeasurementResolver to enable Born rule verification (QM_5): P(outcome k) = \|α_k\|².
`towerSourceLevel`	Object	true	`TowerCompletenessResolver`	`WittLevel`	The level at which the tower starts.
`towerTargetLevel`	Object	true	`TowerCompletenessResolver`	`WittLevel`	The level to which the tower is being built.
`currentChain`	Object	true	`TowerCompletenessResolver`	`LiftChain`	The LiftChain under construction.
`towerStepResolver`	Object	true	`TowerCompletenessResolver`	`IncrementalCompletenessResolver`	The IncrementalCompletenessResolver used for each single-step lift.
`executionPolicy`	Object	true	`SessionResolver`	`ExecutionPolicy`	The ordering strategy this resolver applies to pending queries. Defaults to FifoPolicy if unset.
`homotopyTarget`	Object	true	`HomotopyResolver`	`CechNerve`	The CechNerve whose homotopy type this resolver computes.
`homotopyResult`	Object	false	`HomotopyResolver`	`HomotopyGroup`	A HomotopyGroup observable produced by this resolver.
`moduliTarget`	Object	true	`ModuliResolver`	`CompleteType`	The CompleteType whose local moduli structure this resolver computes.
`moduliDeformation`	Object	true	`ModuliResolver`	`DeformationComplex`	The DeformationComplex constructed by this resolver.
`dispatchTable`	Object	true	`Resolver`	`DispatchTable`	The dispatch table governing resolver selection for this resolver class.
`resolverPredicate`	Object	true	`Resolver`	`TypePredicate`	The predicate that selects this specific resolver. When the predicate evaluates to true on an input type, this resolver is chosen.

Named Individuals

Name	Type	Comment
`ConstantTime`	`ComplexityClass`	O(1) complexity — the resolver runs in constant time regardless of ring size.
`LogarithmicTime`	`ComplexityClass`	O(log n) complexity — the resolver runs in logarithmic time in the quantum level.
`LinearTime`	`ComplexityClass`	O(n) complexity — the resolver runs in time linear in the quantum level.
`ExponentialTime`	`ComplexityClass`	O(2^n) complexity — the resolver runs in time exponential in the quantum level.
`FifoPolicy`	`ExecutionPolicyKind`	Process queries in arrival order. The implicit pre-Amendment 48 behavior.
`MinFreeCountFirst`	`ExecutionPolicyKind`	Process the query with the smallest targetSite.freeRank first. Favors cheapest resolutions, accelerating early grounding gain.
`MaxFreeCountFirst`	`ExecutionPolicyKind`	Process the query with the largest targetSite.freeRank first. Favors hardest resolutions, maximizing information gain per step.
`DisjointFirst`	`ExecutionPolicyKind`	Process queries whose targetSite is disjoint from all other pending queries' site sets first. Minimizes contention when operating against a SharedContext.

UOR Resolvers

Imports

Classes

Properties

Named Individuals

Related Concepts