UOR Type System

IRI
https://uor.foundation/type/
Prefix
type:
Space
user
Comment
Runtime type declarations that parameterize the resolution pipeline. Types are declared by Prism applications and resolved to partitions of the ring.

Imports

  • https://uor.foundation/schema/
  • https://uor.foundation/u/
  • https://uor.foundation/op/

Classes

NameIRISubclass OfDisjoint WithComment
TypeDefinitionhttps://uor.foundation/type/TypeDefinitionhttp://www.w3.org/2002/07/owl#Thinghttps://uor.foundation/type/Constraint, https://uor.foundation/type/MetricAxisA runtime type declaration. The root class for all UOR types. Each TypeDefinition, when resolved, produces a partition of the ring at the specified quantum level.
PrimitiveTypehttps://uor.foundation/type/PrimitiveTypehttps://uor.foundation/type/TypeDefinitionA primitive type defined by a fixed bit width. The carrier is the entire ring Z/(2^n)Z at the specified quantum level.
ProductTypehttps://uor.foundation/type/ProductTypehttps://uor.foundation/type/TypeDefinitionA product (Cartesian) type formed from multiple component types. The carrier is the product of the component carriers.
SumTypehttps://uor.foundation/type/SumTypehttps://uor.foundation/type/TypeDefinitionA sum (disjoint union) type formed from multiple variant types. The carrier is the disjoint union of the variant carriers.
ConstrainedTypehttps://uor.foundation/type/ConstrainedTypehttps://uor.foundation/type/TypeDefinitionA type formed by constraining a base type with a predicate. The carrier is the subset of the base carrier satisfying the constraint.
Constrainthttps://uor.foundation/type/Constrainthttp://www.w3.org/2002/07/owl#Thinghttps://uor.foundation/type/TypeDefinition, https://uor.foundation/type/MetricAxisA composable predicate that refines a type by pinning one or more site coordinates. Constraints are the parameterization mechanism for ConstrainedType.
ResidueConstrainthttps://uor.foundation/type/ResidueConstrainthttps://uor.foundation/type/Constrainthttps://uor.foundation/type/CarryConstraint, https://uor.foundation/type/DepthConstraint, https://uor.foundation/type/CompositeConstraint, https://uor.foundation/type/HammingConstraint, https://uor.foundation/type/SiteConstraint, https://uor.foundation/type/AffineConstraintA constraint based on residue class membership: x ≡ r (mod m). Pins sites corresponding to the residue pattern.
CarryConstrainthttps://uor.foundation/type/CarryConstrainthttps://uor.foundation/type/Constrainthttps://uor.foundation/type/ResidueConstraint, https://uor.foundation/type/DepthConstraint, https://uor.foundation/type/CompositeConstraint, https://uor.foundation/type/HammingConstraint, https://uor.foundation/type/SiteConstraint, https://uor.foundation/type/AffineConstraintA constraint based on carry propagation patterns in ring arithmetic. Pins sites corresponding to carry positions.
DepthConstrainthttps://uor.foundation/type/DepthConstrainthttps://uor.foundation/type/Constrainthttps://uor.foundation/type/ResidueConstraint, https://uor.foundation/type/CarryConstraint, https://uor.foundation/type/CompositeConstraint, https://uor.foundation/type/HammingConstraint, https://uor.foundation/type/SiteConstraint, https://uor.foundation/type/AffineConstraintA constraint on factorization depth: the minimum and maximum number of irreducible factors. Pins sites by bounding the factorization tree depth.
CompositeConstrainthttps://uor.foundation/type/CompositeConstrainthttps://uor.foundation/type/Constrainthttps://uor.foundation/type/ResidueConstraint, https://uor.foundation/type/CarryConstraint, https://uor.foundation/type/DepthConstraint, https://uor.foundation/type/HammingConstraint, https://uor.foundation/type/SiteConstraint, https://uor.foundation/type/AffineConstraintA constraint formed by composing two or more simpler constraints. The composite pins the union of sites pinned by its components.
HammingConstrainthttps://uor.foundation/type/HammingConstrainthttps://uor.foundation/type/Constrainthttps://uor.foundation/type/ResidueConstraint, https://uor.foundation/type/CarryConstraint, https://uor.foundation/type/DepthConstraint, https://uor.foundation/type/CompositeConstraint, https://uor.foundation/type/SiteConstraint, https://uor.foundation/type/AffineConstraintPins the Hamming weight of the Datum to at most the bound. The horizontal axis of the tri-metric.
SiteConstrainthttps://uor.foundation/type/SiteConstrainthttps://uor.foundation/type/Constrainthttps://uor.foundation/type/ResidueConstraint, https://uor.foundation/type/CarryConstraint, https://uor.foundation/type/DepthConstraint, https://uor.foundation/type/CompositeConstraint, https://uor.foundation/type/HammingConstraint, https://uor.foundation/type/AffineConstraintPins a single site coordinate to 0 or 1. The atomic unit of the site budget.
AffineConstrainthttps://uor.foundation/type/AffineConstrainthttps://uor.foundation/type/Constrainthttps://uor.foundation/type/ResidueConstraint, https://uor.foundation/type/CarryConstraint, https://uor.foundation/type/DepthConstraint, https://uor.foundation/type/CompositeConstraint, https://uor.foundation/type/HammingConstraint, https://uor.foundation/type/SiteConstraintPins the Datum to an affine subspace specified by an offset and a set of generators.
MetricAxishttps://uor.foundation/type/MetricAxishttp://www.w3.org/2002/07/owl#Thinghttps://uor.foundation/type/TypeDefinition, https://uor.foundation/type/ConstraintA classification axis for constraints by their geometric effect. The three axes — vertical (ring/additive), horizontal (Hamming/bitwise), diagonal (incompatibility) — form the tri-metric coordinate system of UOR.
CompleteTypehttps://uor.foundation/type/CompleteTypehttps://uor.foundation/type/TypeDefinitionA TypeDefinition certified to satisfy the UOR completeness criterion (IT_7d): its constraint nerve N(C) has Euler characteristic χ = n and all Betti numbers β_k = 0. A CompleteType guarantees that resolution closes the site budget in O(1) — no iterative refinement is required. Completeness is attested by a cert:CompletenessCertificate linked via cert:certifiedType. This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
CompletenessCandidatehttps://uor.foundation/type/CompletenessCandidatehttps://uor.foundation/type/ConstrainedTypehttps://uor.foundation/type/CompleteTypeA ConstrainedType actively undergoing the completeness certification pipeline. Links to the resolver:ResolutionState tracking the current iteration and to the resolver:CechNerve being computed. Disjoint from CompleteType (which is already certified). This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
CompletenessWitnesshttps://uor.foundation/type/CompletenessWitnesshttp://www.w3.org/2002/07/owl#ThingA record of a single site-closing event: one constraint application that reduced the FreeRank deficit. Carries the applied constraint and the sitesClosed count. Forms the ordered audit trail between ConstrainedType and CompleteType.
TypeSynthesisGoalhttps://uor.foundation/type/TypeSynthesisGoalhttp://www.w3.org/2002/07/owl#ThingA specification of the desired topological properties of a type to be synthesised. Carries a target Euler characteristic (targetEulerCharacteristic) and a target Betti profile (zero or more targetBettiNumber assertions). The minimal goal for O(1) resolution is: targetEulerCharacteristic = n and all targetBettiNumber = 0 — the IT_7d profile.
TypeSynthesisResulthttps://uor.foundation/type/TypeSynthesisResulthttp://www.w3.org/2002/07/owl#ThingThe output of a TypeSynthesisResolver run. Contains the SynthesizedType, the realised topological signature (as a SynthesisSignature), and the SynthesisTrace recording the construction steps.
SynthesizedTypehttps://uor.foundation/type/SynthesizedTypehttps://uor.foundation/type/ConstrainedTypeA ConstrainedType produced by the TypeSynthesisResolver. Distinguished from a hand-authored ConstrainedType by the presence of a type:synthesisResult link. May or may not be a CompleteType, depending on the synthesis goal. This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
MinimalConstraintBasishttps://uor.foundation/type/MinimalConstraintBasishttp://www.w3.org/2002/07/owl#ThingThe minimal set of constraints in the SynthesizedType's constraint set that is sufficient to realise the target topological signature. The minimality criterion is that removing any single member changes the realised signature.
WittLifthttps://uor.foundation/type/WittLifthttp://www.w3.org/2002/07/owl#ThingA ConstrainedType T' over R_{n+1} obtained by extending a ConstrainedType T over R_n. Carries a link to the base type (liftBase), the quantum level it lifts to (liftTargetLevel), and the LiftObstruction (if the lift fails to transfer completeness). A WittLift is a CompleteType iff its LiftObstruction is trivial.
LiftObstructionhttps://uor.foundation/type/LiftObstructionhttp://www.w3.org/2002/07/owl#ThingThe algebraic obstruction to a WittLift inheriting the completeness of its base type. Computed as the image of the spectral sequence differential d_2. If trivial (zero), the base type's completeness lifts. If non-trivial, at least one additional constraint is needed at the new quantum level.
TwistedTypehttps://uor.foundation/type/TwistedTypehttps://uor.foundation/type/ConstrainedTypehttps://uor.foundation/type/FlatTypeA ConstrainedType whose HolonomyGroup is non-trivial — at least one closed constraint path produces a non-identity dihedral element. A TwistedType may still be a CompleteType (IT_7d is a homological, not holonomic, criterion), but its resolution paths require tracking dihedral accumulation. This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
FlatTypehttps://uor.foundation/type/FlatTypehttps://uor.foundation/type/ConstrainedTypehttps://uor.foundation/type/TwistedTypeA ConstrainedType whose HolonomyGroup is trivial — all closed constraint paths have identity monodromy. The constraint configuration is topologically flat: resolution is path-independent. This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
SuperposedSiteStatehttps://uor.foundation/type/SuperposedSiteStatehttps://uor.foundation/type/TypeDefinitionA type representing a superposition of site states where sites carry complex amplitudes rather than binary pinned/free assignments. Ontological realisation of RC_5 (Amendment 32). This class is not addressable from a type-expr position in the term language; references from term-language positions are rejected by the resolver.
ForbiddenSignaturehttps://uor.foundation/type/ForbiddenSignaturehttp://www.w3.org/2002/07/owl#ThingA topological signature (χ, β_k) that is formally impossible to achieve for any ConstrainedType. Witnessed by an ImpossibilityWitness in proof/.
CollapsedSiteStatehttps://uor.foundation/type/CollapsedSiteStatehttp://www.w3.org/2002/07/owl#ThingA site state that has undergone projective collapse from a SuperposedSiteState to a definitive classical value. Topologically equivalent to a classically pinned site (QM_2).
LiftChainhttps://uor.foundation/type/LiftChainhttp://www.w3.org/2002/07/owl#ThingAn ordered composition of WittLift steps from liftSourceLevel (Q_j) to liftTargetLevel (Q_k) for any j < k. The canonical object certifying type completeness at arbitrary Q_k.
ObstructionChainhttps://uor.foundation/type/ObstructionChainhttp://www.w3.org/2002/07/owl#ThingThe complete ordered sequence of LiftObstruction records encountered and resolved along a LiftChain. An empty ObstructionChain means the tower is flat.
ModuliSpacehttps://uor.foundation/type/ModuliSpacehttp://www.w3.org/2002/07/owl#ThingThe space of all CompleteTypes over R_n at a given quantum level.
HolonomyStratumhttps://uor.foundation/type/HolonomyStratumhttp://www.w3.org/2002/07/owl#ThingA stratum indexed by a conjugacy class of subgroups of D_{2^n}.
DeformationFamilyhttps://uor.foundation/type/DeformationFamilyhttp://www.w3.org/2002/07/owl#ThingA one-parameter family of constraint configurations parameterizing a path.
VersalDeformationhttps://uor.foundation/type/VersalDeformationhttp://www.w3.org/2002/07/owl#ThingThe versal deformation of a CompleteType T.
ModuliTowerMaphttps://uor.foundation/type/ModuliTowerMaphttp://www.w3.org/2002/07/owl#ThingThe map induced by WittLift from one moduli space to the next.
GaloisConnectionhttps://uor.foundation/type/GaloisConnectionhttp://www.w3.org/2002/07/owl#ThingThe adjunction between the type lattice and the site lattice. The upper adjoint is type closure; the lower adjoint is site interior. σ = lower adjoint evaluation; r = complement of upper adjoint image.
TypeInclusionhttps://uor.foundation/type/TypeInclusionhttps://uor.foundation/morphism/TransformA morphism T₁ → T₂ witnessing that T₁ is a subtype of T₂: the constraint set of T₁ is a superset of the constraint set of T₂.
VarianceAnnotationhttps://uor.foundation/type/VarianceAnnotationhttp://www.w3.org/2002/07/owl#ThingThe variance of a structural type position under operad composition. One of Covariant, Contravariant, Invariant, or Bivariant.
SubtypingLatticehttps://uor.foundation/type/SubtypingLatticehttp://www.w3.org/2002/07/owl#ThingThe partial order on types induced by TypeInclusion. The top element is PrimitiveType (no constraints); the bottom elements are CompleteTypes (all sites pinned).

Properties

NameKindFunctionalDomainRangeComment
bitWidthDatatypetruehttps://uor.foundation/type/PrimitiveTypehttp://www.w3.org/2001/XMLSchema#positiveIntegerThe bit width of a primitive type (the quantum level n). The carrier is Z/(2^n)Z.
componentObjectfalsehttps://uor.foundation/type/ProductTypehttps://uor.foundation/type/TypeDefinitionA component type in a product type.
baseTypeObjecttruehttps://uor.foundation/type/ConstrainedTypehttps://uor.foundation/type/TypeDefinitionThe base type that a constrained type restricts.
contentAddressObjecttruehttps://uor.foundation/type/TypeDefinitionhttps://uor.foundation/u/ElementThe content-derived address of this type definition, uniquely identifying the type in the UOR address space.
hasConstraintObjectfalsehttps://uor.foundation/type/ConstrainedTypehttps://uor.foundation/type/ConstraintA typed constraint object applied to this constrained type. Replaces the deprecated string-based type:constraint property.
modulusDatatypetruehttps://uor.foundation/type/ResidueConstrainthttp://www.w3.org/2001/XMLSchema#positiveIntegerThe modulus m of a residue constraint: x ≡ r (mod m).
residueDatatypetruehttps://uor.foundation/type/ResidueConstrainthttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe residue value r of a residue constraint: x ≡ r (mod m).
carryPatternObjecttruehttps://uor.foundation/type/CarryConstrainthttps://uor.foundation/schema/DatumThe carry propagation pattern of a carry constraint, expressed as a Datum at the appropriate quantum level.
minDepthDatatypetruehttps://uor.foundation/type/DepthConstrainthttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe minimum factorization depth required by a depth constraint.
maxDepthDatatypetruehttps://uor.foundation/type/DepthConstrainthttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe maximum factorization depth allowed by a depth constraint.
composedFromObjectfalsehttps://uor.foundation/type/CompositeConstrainthttps://uor.foundation/type/ConstraintA component constraint of this composite constraint.
hammingBoundDatatypetruehttps://uor.foundation/type/HammingConstrainthttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerUpper bound on the Hamming weight of the Datum.
siteIndexDatatypetruehttps://uor.foundation/type/SiteConstrainthttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerZero-based index of the pinned site coordinate.
siteValueObjecttruehttps://uor.foundation/type/SiteConstrainthttps://uor.foundation/schema/DatumThe value the pinned site coordinate must equal (a Datum in the set {0, 1}).
affineOffsetObjecttruehttps://uor.foundation/type/AffineConstrainthttps://uor.foundation/schema/DatumConstant offset defining the affine subspace.
affineGeneratorObjectfalsehttps://uor.foundation/type/AffineConstrainthttps://uor.foundation/schema/DatumA generator of the affine subspace. Non-functional: multiple generators span the subspace.
metricAxisObjecttruehttps://uor.foundation/type/Constrainthttps://uor.foundation/type/MetricAxisThe metric axis along which this constraint operates: vertical (ring), horizontal (Hamming), or diagonal (incompatibility).
pinsSitesObjectfalsehttps://uor.foundation/type/Constrainthttps://uor.foundation/partition/SiteIndexA site coordinate that this constraint pins when applied.
affectsAxisObjectfalsehttps://uor.foundation/op/Operationhttps://uor.foundation/type/MetricAxisThe metric axis that this operation affects. Replaces the string-valued type:axisSignature property with a typed reference to MetricAxis individuals. Non-functional: an operation may affect multiple axes.
crossingCostDatatypetruehttps://uor.foundation/type/Constrainthttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe cost of applying this constraint in terms of axis crossings: the number of metric boundaries that must be traversed.
completenessCandidateObjectfalsehttps://uor.foundation/type/CompletenessCandidatehttps://uor.foundation/type/ConstrainedTypeThe ConstrainedType being evaluated for completeness by this CompletenessCandidate.
candidateNerveObjecttruehttps://uor.foundation/type/CompletenessCandidatehttps://uor.foundation/resolver/CechNerveThe constraint nerve being computed for this candidate. The CompletenessResolver reads χ(N(C)) from this nerve at each iteration via resolver:nerveEulerCharacteristic.
witnessConstraintObjecttruehttps://uor.foundation/type/CompletenessWitnesshttps://uor.foundation/type/ConstraintThe constraint applied in this witness step.
sitesClosedDatatypetruehttps://uor.foundation/type/CompletenessWitnesshttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerNumber of sites closed by this witness step.
targetEulerCharacteristicDatatypetruehttps://uor.foundation/type/TypeSynthesisGoalhttp://www.w3.org/2001/XMLSchema#integerThe target χ(N(C)) value. For O(1) resolution: set equal to n (the quantum level).
targetBettiNumberDatatypefalsehttps://uor.foundation/type/TypeSynthesisGoalhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerNon-functional. Each assertion specifies a target Betti number value for a given homological degree. Multiple assertions permitted, one per degree.
synthesisResultObjecttruehttps://uor.foundation/type/SynthesizedTypehttps://uor.foundation/type/TypeSynthesisResultLinks a SynthesizedType back to the synthesis run that produced it.
basisConstraintObjectfalsehttps://uor.foundation/type/MinimalConstraintBasishttps://uor.foundation/type/ConstraintNon-functional. One assertion per constraint in the minimal basis.
basisSizeDatatypetruehttps://uor.foundation/type/MinimalConstraintBasishttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe cardinality of the minimal basis. The theoretical lower bound is n (one constraint per site).
liftBaseObjecttruehttps://uor.foundation/type/WittLifthttps://uor.foundation/type/ConstrainedTypeThe base type being lifted to the next quantum level.
liftTargetLevelObjecttruehttps://uor.foundation/type/WittLifthttps://uor.foundation/schema/WittLevelThe quantum level this lift targets.
liftObstructionObjecttruehttps://uor.foundation/type/WittLifthttps://uor.foundation/type/LiftObstructionThe LiftObstruction for this lift. Trivial (zero class) iff the lift inherits completeness.
obstructionTrivialDatatypetruehttps://uor.foundation/type/LiftObstructionhttp://www.w3.org/2001/XMLSchema#booleanTrue iff the obstruction class is zero — the base type's completeness transfers to the lifted quantum level without additional constraints.
obstructionSiteObjecttruehttps://uor.foundation/type/LiftObstructionhttps://uor.foundation/partition/SiteIndexThe site at the new quantum level where the obstruction is located. Ranges over the new bit position introduced at Q_{n+1}.
holonomyGroupObjecttruehttps://uor.foundation/type/ConstrainedTypehttps://uor.foundation/observable/HolonomyGroupThe HolonomyGroup of this type. Computed by the MonodromyResolver.
monodromyClassObjecttruehttps://uor.foundation/type/ConstrainedTypehttps://uor.foundation/observable/MonodromyClassThe MonodromyClass classifying this type as flat or twisted.
amplitudeDatatypetruehttps://uor.foundation/type/SuperposedSiteStatehttp://www.w3.org/2001/XMLSchema#decimalThe amplitude coefficient for this superposed site state.
targetForbiddenDatatypetruehttps://uor.foundation/type/TypeSynthesisGoalhttp://www.w3.org/2001/XMLSchema#booleanWhether the target signature of this TypeSynthesisGoal is a ForbiddenSignature. If true, synthesis is provably impossible.
collapsedFromObjecttruehttps://uor.foundation/type/CollapsedSiteStatehttps://uor.foundation/type/SuperposedSiteStateThe SuperposedSiteState from which this CollapsedSiteState was produced by projective measurement.
survivingAmplitudeDatatypetruehttps://uor.foundation/type/CollapsedSiteStatehttp://www.w3.org/2001/XMLSchema#decimalThe amplitude of the surviving branch after projective collapse. |α|² is the probability of this outcome under the Born rule.
normalizationVerifiedDatatypetruehttps://uor.foundation/type/SuperposedSiteStatehttp://www.w3.org/2001/XMLSchema#booleanWhether the amplitude vector of this SuperposedSiteState satisfies the normalization condition Σ|αᵢ|² = 1 (QM_5). Set by the SuperpositionResolver after verification.
holonomyClassifiedDatatypetruehttps://uor.foundation/type/ConstrainedTypehttp://www.w3.org/2001/XMLSchema#booleanWhether this ConstrainedType has been classified as FlatType or TwistedType by the MonodromyResolver. The MN_8 identity guarantees this is a bivalent classification: holonomyClassified(T) iff isFlatType(T) xor isTwistedType(T).
liftSourceLevelObjecttruehttps://uor.foundation/type/LiftChainhttps://uor.foundation/schema/WittLevelThe quantum level at the base of the chain.
chainLengthDatatypetruehttps://uor.foundation/type/LiftChainhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe number of WittLift steps in the chain (k - j).
chainStepObjectfalsehttps://uor.foundation/type/LiftChainhttps://uor.foundation/type/WittLiftA WittLift step in this chain. Non-functional: one per step.
chainObstructionProfileObjecttruehttps://uor.foundation/type/LiftChainhttps://uor.foundation/type/ObstructionChainThe full obstruction history of this chain.
resolvedBasisSizeDatatypetruehttps://uor.foundation/type/LiftChainhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe basis size of the CompleteType at the chain target level.
obstructionAtObjectfalsehttps://uor.foundation/type/ObstructionChainhttps://uor.foundation/type/LiftObstructionA non-trivial LiftObstruction in this chain. Non-functional.
obstructionCountDatatypetruehttps://uor.foundation/type/ObstructionChainhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerTotal number of non-trivial LiftObstruction records.
isFlatDatatypetruehttps://uor.foundation/type/ObstructionChainhttp://www.w3.org/2001/XMLSchema#booleanTrue iff obstructionCount = 0 (flat tower).
moduliWittLevelObjecttruehttps://uor.foundation/type/ModuliSpacehttps://uor.foundation/schema/WittLevelThe quantum level at which this moduli space is defined.
moduliPointObjectfalsehttps://uor.foundation/type/ModuliSpacehttps://uor.foundation/type/CompleteTypeA CompleteType that is a point of this moduli space.
moduliDimensionDatatypetruehttps://uor.foundation/type/ModuliSpacehttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe dimension of this moduli space.
stratumHolonomyClassObjecttruehttps://uor.foundation/type/HolonomyStratumhttps://uor.foundation/observable/MonodromyClassThe MonodromyClass indexing this stratum.
stratumCodimensionDatatypetruehttps://uor.foundation/type/HolonomyStratumhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe codimension of this stratum within the moduli space.
stratumModuliObjecttruehttps://uor.foundation/type/HolonomyStratumhttps://uor.foundation/type/ModuliSpaceThe moduli space containing this stratum.
familyParameterObjectfalsehttps://uor.foundation/type/DeformationFamilyhttps://uor.foundation/type/CompleteTypeA CompleteType along the deformation path.
familyPreservesCompletenessDatatypetruehttps://uor.foundation/type/DeformationFamilyhttp://www.w3.org/2001/XMLSchema#booleanWhether every member of this deformation family remains a CompleteType.
versalBaseObjecttruehttps://uor.foundation/type/VersalDeformationhttps://uor.foundation/type/CompleteTypeThe CompleteType at the base of this versal deformation.
versalDimensionDatatypetruehttps://uor.foundation/type/VersalDeformationhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe dimension of the versal deformation space.
towerMapSourceObjecttruehttps://uor.foundation/type/ModuliTowerMaphttps://uor.foundation/type/ModuliSpaceThe source moduli space of this tower map.
upperAdjointObjecttruehttps://uor.foundation/type/GaloisConnectionhttps://uor.foundation/schema/TermExpressionThe upper adjoint (type closure) of the Galois connection, expressed as a symbolic formula string.
lowerAdjointObjecttruehttps://uor.foundation/type/GaloisConnectionhttps://uor.foundation/schema/TermExpressionThe lower adjoint (site interior) of the Galois connection, expressed as a symbolic formula string.
fixpointConditionObjecttruehttps://uor.foundation/type/GaloisConnectionhttps://uor.foundation/schema/TermExpressionThe fixpoint condition for the Galois connection: when upper(lower(T)) = T, the type is complete.
refinementDirectionDatatypetruehttps://uor.foundation/type/GaloisConnectionhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerDescription of the refinement direction: ascending in type lattice corresponds to descending in site freedom.
structuralSiteCountAnnotationtrue—http://www.w3.org/2001/XMLSchema#stringFormula or description of the site count for a structural type individual.
structuralGroundingAnnotationtrue—http://www.w3.org/2001/XMLSchema#stringDescription of the grounding rule that maps values of this structural type onto the UOR ring.
structuralConstraintAnnotationtrue—http://www.w3.org/2001/XMLSchema#stringDescription of the constraint characterizing this structural type, if applicable.
galoisClosurePropertyObjecttruehttps://uor.foundation/type/GaloisConnectionhttps://uor.foundation/schema/TermExpressionThe closure property of a Galois connection.
galoisInteriorPropertyObjecttruehttps://uor.foundation/type/GaloisConnectionhttps://uor.foundation/schema/TermExpressionThe interior property of a Galois connection.
groundingMapRefObjecttrue—https://uor.foundation/morphism/GroundingMapReference to the grounding map used for this type.
compositionLawObjecttrue—https://uor.foundation/schema/TermExpressionThe algebraic composition law governing this type.
siteOrderingConstraintObjecttrue—https://uor.foundation/schema/TermExpressionConstraint on the ordering of sites for this type.
backboneThresholdDatatypetrue—http://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe threshold for backbone inclusion in the type lattice.
permutationGroupObjecttrue—https://uor.foundation/op/GroupThe permutation group acting on sites of this type.
acyclicityWitnessDatatypetrue—http://www.w3.org/2001/XMLSchema#booleanWitness certifying acyclicity of the type dependency graph.
connectivityWitnessDatatypetrue—http://www.w3.org/2001/XMLSchema#booleanWitness certifying connectivity of the type graph.
schemaConstraintObjecttrue—https://uor.foundation/schema/TermExpressionConstraint imposed by the schema on this type.
alphabetSizeAnnotationtrue—http://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe size of the alphabet for symbol-based types.
quantizationRangeObjecttrue—https://uor.foundation/schema/TermExpressionThe range specification for quantized types.
elementTypeRefObjecttrue—https://uor.foundation/type/TypeDefinitionReference to the element type within a composite type.
inclusionSourceObjecttruehttps://uor.foundation/type/TypeInclusionhttps://uor.foundation/type/ConstrainedTypeThe subtype (more constraints).
inclusionTargetObjecttruehttps://uor.foundation/type/TypeInclusionhttps://uor.foundation/type/ConstrainedTypeThe supertype (fewer constraints).
positionVarianceObjecttruehttps://uor.foundation/operad/StructuralOperadhttps://uor.foundation/type/VarianceAnnotationThe variance of each operand position.
inclusionWitnessDatatypetruehttps://uor.foundation/type/TypeInclusionhttp://www.w3.org/2001/XMLSchema#booleanTrue iff constraints(source) ⊇ constraints(target). Computed, not asserted.
latticeDepthDatatypetruehttps://uor.foundation/type/SubtypingLatticehttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerMaximum chain length from PrimitiveType (top) to any CompleteType (bottom). Equals the site budget n at quantum level Q_k.

Named Individuals

NameTypePropertiesComment
verticalAxishttps://uor.foundation/type/MetricAxis—The vertical (ring/additive) metric axis. Constraints on this axis operate through ring arithmetic: residue classes, divisibility, and additive structure.
horizontalAxishttps://uor.foundation/type/MetricAxis—The horizontal (Hamming/bitwise) metric axis. Constraints on this axis operate through bitwise structure: carry patterns, bit positions, and Hamming distance.
diagonalAxishttps://uor.foundation/type/MetricAxis—The diagonal (incompatibility) metric axis. Constraints on this axis measure the gap between ring and Hamming metrics — the curvature of UOR geometry.
ScalarTypehttps://uor.foundation/type/PrimitiveType
  • structuralSiteCount: n (quantization bits)
  • structuralGrounding: quantize(value, range, bits) produces ring element where d_R reflects value proximity
A single value from an ordered domain. siteCount = n (quantization bits).
SymbolTypehttps://uor.foundation/type/PrimitiveType
  • structuralSiteCount: ceil(log2(|alphabet|))
  • structuralGrounding: argmin_{encoding} sum d_delta over observed pairs (CY_5)
A value from a finite unordered set. siteCount = ceil(log2(|alphabet|)).
SequenceTypehttps://uor.foundation/type/ProductType
  • structuralSiteCount: sum of element site counts
  • structuralGrounding: free monoid on element type, backbone constraint
  • structuralConstraint: backbone ordering: elements indexed by position
An ordered list of elements with backbone constraint. The free monoid on the element type.
TupleTypehttps://uor.foundation/type/ProductType
  • structuralSiteCount: sum of field site counts
  • structuralGrounding: site ordering follows CY_6 (optimal site ordering)
A fixed collection of named fields.
GraphTypehttps://uor.foundation/type/ConstrainedType
  • structuralSiteCount: sum of node site counts + edge overhead
  • structuralGrounding: constraint nerve = graph nerve, beta_k equality
  • structuralConstraint: edge constraints: adjacency preserved under grounding
Nodes with edge constraints. Constraint nerve = graph topology.
SetTypehttps://uor.foundation/type/ConstrainedType
  • structuralSiteCount: sum of element site counts
  • structuralGrounding: d_delta invariant under element permutation, D_{2n} symmetry
  • structuralConstraint: permutation invariance: encoding is order-independent
Unordered collection. d_delta is permutation-invariant.
TreeTypehttps://uor.foundation/type/ConstrainedType
  • structuralSiteCount: sum of node site counts
  • structuralGrounding: parent-child encoding with acyclicity constraint
  • structuralConstraint: beta_1=0 (acyclic), beta_0=1 (connected)
Hierarchical structure. beta_1=0 (acyclic), beta_0=1 (connected).
TableTypehttps://uor.foundation/type/ProductType
  • structuralSiteCount: row_count * tuple_site_count
  • structuralGrounding: Sequence(Tuple(S)), functorial decomposition
  • structuralConstraint: shared schema: all rows conform to tuple type S
Collection of tuples sharing a schema = Sequence(Tuple(S)). Functorial decomposition.
Covarianthttps://uor.foundation/type/VarianceAnnotation
  • enumVariant: https://uor.foundation/type/Covariant
The structural position preserves TypeInclusion: if T₁ ≤ T₂, then F(T₁) ≤ F(T₂).
Contravarianthttps://uor.foundation/type/VarianceAnnotation
  • enumVariant: https://uor.foundation/type/Contravariant
The structural position reverses TypeInclusion: if T₁ ≤ T₂, then F(T₂) ≤ F(T₁).
Invarianthttps://uor.foundation/type/VarianceAnnotation
  • enumVariant: https://uor.foundation/type/Invariant
The structural position requires exact type equality: F(T₁) ≤ F(T₂) only if T₁ = T₂.
Bivarianthttps://uor.foundation/type/VarianceAnnotation
  • enumVariant: https://uor.foundation/type/Bivariant
The structural position ignores the type parameter: F(T₁) ≤ F(T₂) for all T₁, T₂.
EitherTypehttps://uor.foundation/type/SumType—The canonical binary disjoint union type whose carrier is L + R.
OptionTypehttps://uor.foundation/type/SumType—The canonical A + Unit idiom for optional values.