UOR Certificates

IRI
https://uor.foundation/cert/
Prefix
cert:
Space
bridge
Comment
Kernel-produced attestation certificates for transforms, isometries, and involutions. Each certificate verifies that a specific structural property holds.

Imports

  • https://uor.foundation/op/
  • https://uor.foundation/proof/
  • https://uor.foundation/schema/
  • https://uor.foundation/type/

Classes

NameIRISubclass OfDisjoint WithComment
Certificatehttps://uor.foundation/cert/Certificatehttp://www.w3.org/2002/07/owl#ThingA kernel-produced attestation. The root class for all certificate types.
TransformCertificatehttps://uor.foundation/cert/TransformCertificatehttps://uor.foundation/cert/CertificateA certificate attesting to the properties of a morphism:Transform. Certifies that the transform maps source to target correctly.
IsometryCertificatehttps://uor.foundation/cert/IsometryCertificatehttps://uor.foundation/cert/CertificateA certificate attesting that a morphism:Isometry preserves metric distances. Certifies the transform is a metric isometry with respect to the specified metric.
InvolutionCertificatehttps://uor.foundation/cert/InvolutionCertificatehttps://uor.foundation/cert/CertificateA certificate attesting that an operation is an involution: f(f(x)) = x for all x in R_n.
CompletenessCertificatehttps://uor.foundation/cert/CompletenessCertificatehttps://uor.foundation/cert/CertificateA certificate attesting that a type:CompleteType satisfies IT_7d: its constraint nerve has χ = n and all Betti numbers β_k = 0. Issued by the kernel after running the full ψ pipeline on the type's constraint set.
CompletenessAuditTrailhttps://uor.foundation/cert/CompletenessAuditTrailhttp://www.w3.org/2002/07/owl#ThingAn ordered collection of CompletenessWitness records belonging to a CompletenessCertificate. Provides full provenance of the certification process: every constraint applied, every site closed, in sequence.
GroundingCertificatehttps://uor.foundation/cert/GroundingCertificatehttps://uor.foundation/cert/CertificateA certificate attesting that a state:GroundedContext has reached full saturation (σ = 1, freeRank = 0, S = 0, T_ctx = 0) per SC_4. The session-layer dual of CompletenessCertificate.
GeodesicCertificatehttps://uor.foundation/cert/GeodesicCertificatehttps://uor.foundation/cert/CertificateA certificate attesting that a trace:GeodesicTrace satisfies both GD_1 conditions: AR_1-ordered and DC_10-selected. Transforms ComputationTrace from descriptive to normative.
MeasurementCertificatehttps://uor.foundation/cert/MeasurementCertificatehttps://uor.foundation/cert/CertificateA certificate attesting that a trace:MeasurementEvent respected the von Neumann–Landauer bridge (QM_1): preCollapseEntropy = postCollapseLandauerCost at β* = ln 2.
GeodesicEvidenceBundlehttps://uor.foundation/cert/GeodesicEvidenceBundlehttp://www.w3.org/2002/07/owl#ThingA structured evidence bundle attesting that each sub-predicate of the geodesic condition (GD_6) holds independently: isAR1Ordered and isDC10Selected. Linked from GeodesicCertificate via evidenceBundle.
BornRuleVerificationhttps://uor.foundation/cert/BornRuleVerificationhttps://uor.foundation/cert/CertificateA certificate attesting that a MeasurementEvent outcome probability matches the Born rule: P(outcome k) = |α_k|² (QM_5). Linked from MeasurementCertificate to provide probability distribution verification.
LiftChainCertificatehttps://uor.foundation/cert/LiftChainCertificatehttps://uor.foundation/cert/CertificateA kernel-issued certificate attesting that a LiftChain from liftSourceLevel to liftTargetLevel is complete.
ChainAuditTrailhttps://uor.foundation/cert/ChainAuditTrailhttp://www.w3.org/2002/07/owl#ThingAn ordered collection of per-step evidence records for a LiftChainCertificate.
InhabitanceCertificatehttps://uor.foundation/cert/InhabitanceCertificatehttps://uor.foundation/proof/ComputationCertificate, https://uor.foundation/cert/CertificateA ComputationCertificate verdict primitive that decides carrier non-emptiness on a type:ConstrainedType. Distinct from cert:CompletenessCertificate, which decides freeRank = 0 on the minimal basis. For ConstrainedType instances admitting multiple satisfying value tuples, InhabitanceCertificate.verified may be true while CompletenessCertificate.verified is false.
MultiplicationCertificatehttps://uor.foundation/cert/MultiplicationCertificatehttps://uor.foundation/cert/CertificateA certificate attesting the cost-optimal Toom-Cook splitting factor R for a Datum<L> × Datum<L> multiplication at a given call-site context (stack budget, const-eval regime). Carries the chosen splitting factor, the recursive sub-multiplication count, and the accumulated Landauer cost in nats (priced per op:OA_5). Produced by resolver:MultiplicationResolver.
PartitionCertificatehttps://uor.foundation/cert/PartitionCertificatehttps://uor.foundation/cert/CertificateA certificate attesting the partition component classification of a Datum, assigning it to one of Irreducible, Reducible, Units, or Exterior via the partition:PartitionComponent enumeration. Produced by the bridge partition walk during grounding.
GenericImpossibilityCertificatehttps://uor.foundation/cert/GenericImpossibilityCertificatehttps://uor.foundation/cert/CertificateA certificate attesting that a resolver's verdict path produced a generic impossibility witness — the input failed the resolver's admissibility precondition or decision procedure in a way not covered by a more-specific witness. Returned by every Phase D resolver on failure.
InhabitanceImpossibilityCertificatehttps://uor.foundation/cert/InhabitanceImpossibilityCertificatehttps://uor.foundation/cert/CertificateA certificate attesting that the inhabitance decider concluded the input is unsatisfiable — there is no value in the carrier that satisfies the declared constraint conjunction. Returned by `resolver::inhabitance::certify` on failure.

Properties

NameKindFunctionalDomainRangeComment
transformTypeObjecttruehttps://uor.foundation/cert/TransformCertificatehttps://uor.foundation/schema/TermExpressionThe type of transform this certificate attests to (e.g., 'isometry', 'embedding', 'action').
methodObjecttruehttps://uor.foundation/cert/Certificatehttps://uor.foundation/proof/ProofStrategyThe verification method used to produce this certificate (e.g., 'exhaustive_check', 'symbolic_proof', 'sampling').
operationObjecttruehttps://uor.foundation/cert/InvolutionCertificatehttps://uor.foundation/op/OperationThe operation this certificate applies to.
verifiedDatatypetruehttps://uor.foundation/cert/Certificatehttp://www.w3.org/2001/XMLSchema#booleanWhether this certificate has been verified by the kernel.
wittLengthDatatypetruehttps://uor.foundation/cert/Certificatehttp://www.w3.org/2001/XMLSchema#positiveIntegerThe Witt level at which this certificate was produced.
timestampDatatypetruehttps://uor.foundation/cert/Certificatehttp://www.w3.org/2001/XMLSchema#dateTimeThe time at which this certificate was issued.
certifiesObjecttruehttps://uor.foundation/cert/Certificatehttp://www.w3.org/2002/07/owl#ThingThe resource this certificate attests to. Links a certificate to the observable, transform, or other entity it covers.
certifiedTypeObjecttruehttps://uor.foundation/cert/CompletenessCertificatehttps://uor.foundation/type/CompleteTypeThe TypeDefinition whose completeness this certificate attests. The kernel issues this certificate after running the ψ pipeline on the type's constraint set and confirming IT_7d.
auditTrailObjecttruehttps://uor.foundation/cert/CompletenessCertificatehttps://uor.foundation/cert/CompletenessAuditTrailThe audit trail attesting the certification provenance. Links a CompletenessCertificate to its ordered sequence of CompletenessWitness records.
witnessCountDatatypetruehttps://uor.foundation/cert/CompletenessAuditTrailhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerTotal number of witness steps in this audit trail.
certifiedGroundingObjecttruehttps://uor.foundation/cert/GroundingCertificatehttps://uor.foundation/state/GroundedContextThe GroundedContext whose full saturation this certificate attests. Uses IRI string (cert cannot import state).
groundingWitnessObjecttruehttps://uor.foundation/cert/GroundingCertificatehttps://uor.foundation/state/GroundingWitnessThe GroundingWitness providing step-by-step evidence of the saturation process.
certifiedGeodesicObjecttruehttps://uor.foundation/cert/GeodesicCertificatehttps://uor.foundation/trace/GeodesicTraceThe GeodesicTrace whose geodesic status this certificate attests. Uses IRI string (cert cannot import trace).
geodesicTraceObjecttruehttps://uor.foundation/cert/GeodesicCertificatehttps://uor.foundation/trace/GeodesicTraceThe computation trace that this GeodesicCertificate covers. Redundant with certifiedGeodesic but expresses the inverse direction for queryability.
certifiedMeasurementObjecttruehttps://uor.foundation/cert/MeasurementCertificatehttps://uor.foundation/trace/MeasurementEventThe MeasurementEvent whose QM_1 compliance this certificate attests. Uses IRI string (cert cannot import trace).
vonNeumannEntropyDatatypetruehttps://uor.foundation/cert/MeasurementCertificatehttp://www.w3.org/2001/XMLSchema#decimalThe von Neumann entropy S_vN of the pre-measurement SuperposedSiteState, recorded by this certificate.
landauerCostDatatypetruehttps://uor.foundation/cert/MeasurementCertificatehttp://www.w3.org/2001/XMLSchema#decimalThe Landauer cost incurred by the projective collapse, recorded by this certificate. Equals vonNeumannEntropy at β* = ln 2 per QM_1.
evidenceBundleObjecttruehttps://uor.foundation/cert/GeodesicCertificatehttps://uor.foundation/cert/GeodesicEvidenceBundleThe GeodesicEvidenceBundle attesting to the decomposed sub-predicates (isAR1Ordered, isDC10Selected) of this GeodesicCertificate's geodesic claim.
bornRuleVerifiedDatatypetruehttps://uor.foundation/cert/BornRuleVerificationhttp://www.w3.org/2001/XMLSchema#booleanWhether this BornRuleVerification certificate confirms that all outcome probabilities match the Born rule (QM_5): P(k) = |α_k|² for every site k.
certifiedChainObjecttruehttps://uor.foundation/cert/LiftChainCertificatehttps://uor.foundation/type/LiftChainThe LiftChain this certificate attests to.
chainAuditTrailObjecttruehttps://uor.foundation/cert/LiftChainCertificatehttps://uor.foundation/cert/ChainAuditTrailThe ordered per-step evidence for this certificate.
targetLevelObjecttruehttps://uor.foundation/cert/LiftChainCertificatehttps://uor.foundation/schema/WittLevelThe quantum level Q_k at which the certificate was issued.
sourceLevelObjecttruehttps://uor.foundation/cert/LiftChainCertificatehttps://uor.foundation/schema/WittLevelThe quantum level Q_j from which the tower was started.
chainStepCountDatatypetruehttps://uor.foundation/cert/ChainAuditTrailhttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerNumber of lift steps in this ChainAuditTrail. Must equal chainLength of the certified LiftChain. Distinct from witnessCount (domain-locked to CompletenessAuditTrail).
isAR1OrderedDatatypetruehttps://uor.foundation/cert/GeodesicEvidenceBundlehttp://www.w3.org/2001/XMLSchema#booleanTrue iff the linked GeodesicTrace is ordered by the AR_1 canonical rewriting rule (smallest lexicographic representative first).
isDC10SelectedDatatypetruehttps://uor.foundation/cert/GeodesicEvidenceBundlehttp://www.w3.org/2001/XMLSchema#booleanTrue iff each constraint in the trace was selected by the DC_10 Jacobian oracle at the step where it was applied.
witnessObjectfalsehttps://uor.foundation/cert/InhabitanceCertificatehttps://uor.foundation/schema/ValueTupleA specific value tuple in the carrier when verified is true; absent otherwise. The witness form for cert:InhabitanceCertificate.
searchTraceObjecttruehttps://uor.foundation/cert/InhabitanceCertificatehttps://uor.foundation/trace/InhabitanceSearchTraceThe audit trail of the inhabitance search that produced this certificate.
groundedObjecttruehttps://uor.foundation/cert/InhabitanceCertificatehttps://uor.foundation/type/ConstrainedTypeThe type:ConstrainedType this InhabitanceCertificate is issued for.
splittingFactorDatatypetruehttps://uor.foundation/cert/MultiplicationCertificatehttp://www.w3.org/2001/XMLSchema#positiveIntegerThe Toom-Cook splitting factor R chosen by the multiplication resolver. R = 1 is schoolbook (the const-eval bottom-out); R = 2 is Karatsuba; R >= 3 is Toom-k. The resolver picks the cost-optimal R subject to the call-site's stack budget and const-eval depth constraints.
subMultiplicationCountDatatypetruehttps://uor.foundation/cert/MultiplicationCertificatehttp://www.w3.org/2001/XMLSchema#nonNegativeIntegerThe number of recursive sub-multiplications the chosen splitting factor induces for one Datum<L> × Datum<L> multiplication at this call site. For splitting factor R, the count is (2R - 1) for R > 1, and 1 for R = 1.
landauerCostNatsDatatypetruehttps://uor.foundation/cert/MultiplicationCertificatehttp://www.w3.org/2001/XMLSchema#decimalThe accumulated Landauer cost of the certified multiplication in nats, priced per op:OA_5 (each irreversible bit erasure costs ln 2 nats in the Archimedean completion). Unit: observable:Nats. The value is an xsd:decimal.