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.

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 · Proofs, Derivations & Traces

Class hierarchy
Class hierarchy for UOR Certificates namespace Certificate TransformCerti IsometryCertif InvolutionCert CompletenessCe CompletenessAu GroundingCerti GeodesicCertif MeasurementCer GeodesicEviden BornRuleVerifi LiftChainCerti ChainAuditTrai InhabitanceCer Multiplication PartitionCerti GenericImpossi InhabitanceImp

Imports

Classes

NameSubclass OfDisjoint WithComment
CertificateThingA kernel-produced attestation. The root class for all certificate types.
TransformCertificateCertificateA certificate attesting to the properties of a morphism:Transform. Certifies that the transform maps source to target correctly.
IsometryCertificateCertificateA certificate attesting that a morphism:Isometry preserves metric distances. Certifies the transform is a metric isometry with respect to the specified metric.
InvolutionCertificateCertificateA certificate attesting that an operation is an involution: f(f(x)) = x for all x in R_n.
CompletenessCertificateCertificateA 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.
CompletenessAuditTrailThingAn ordered collection of CompletenessWitness records belonging to a CompletenessCertificate. Provides full provenance of the certification process: every constraint applied, every site closed, in sequence.
GroundingCertificateCertificateA 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.
GeodesicCertificateCertificateA certificate attesting that a trace:GeodesicTrace satisfies both GD_1 conditions: AR_1-ordered and DC_10-selected. Transforms ComputationTrace from descriptive to normative.
MeasurementCertificateCertificateA certificate attesting that a trace:MeasurementEvent respected the von Neumann–Landauer bridge (QM_1): preCollapseEntropy = postCollapseLandauerCost at β* = ln 2.
GeodesicEvidenceBundleThingA structured evidence bundle attesting that each sub-predicate of the geodesic condition (GD_6) holds independently: isAR1Ordered and isDC10Selected. Linked from GeodesicCertificate via evidenceBundle.
BornRuleVerificationCertificateA 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.
LiftChainCertificateCertificateA kernel-issued certificate attesting that a LiftChain from liftSourceLevel to liftTargetLevel is complete.
ChainAuditTrailThingAn ordered collection of per-step evidence records for a LiftChainCertificate.
InhabitanceCertificateComputationCertificate, 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.
MultiplicationCertificateCertificateA 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.
PartitionCertificateCertificateA 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.
GenericImpossibilityCertificateCertificateA 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.
InhabitanceImpossibilityCertificateCertificateA 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
transformTypeObjecttrueTransformCertificateTermExpressionThe type of transform this certificate attests to (e.g., 'isometry', 'embedding', 'action').
methodObjecttrueCertificateProofStrategyThe verification method used to produce this certificate (e.g., 'exhaustive_check', 'symbolic_proof', 'sampling').
operationObjecttrueInvolutionCertificateOperationThe operation this certificate applies to.
verifiedDatatypetrueCertificatebooleanWhether this certificate has been verified by the kernel.
wittLengthDatatypetrueCertificatepositiveIntegerThe Witt level at which this certificate was produced.
timestampDatatypetrueCertificatedateTimeThe time at which this certificate was issued.
certifiesObjecttrueCertificateThingThe resource this certificate attests to. Links a certificate to the observable, transform, or other entity it covers.
certifiedTypeObjecttrueCompletenessCertificateCompleteTypeThe 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.
auditTrailObjecttrueCompletenessCertificateCompletenessAuditTrailThe audit trail attesting the certification provenance. Links a CompletenessCertificate to its ordered sequence of CompletenessWitness records.
witnessCountDatatypetrueCompletenessAuditTrailnonNegativeIntegerTotal number of witness steps in this audit trail.
certifiedGroundingObjecttrueGroundingCertificateGroundedContextThe GroundedContext whose full saturation this certificate attests. Uses IRI string (cert cannot import state).
groundingWitnessObjecttrueGroundingCertificateGroundingWitnessThe GroundingWitness providing step-by-step evidence of the saturation process.
certifiedGeodesicObjecttrueGeodesicCertificateGeodesicTraceThe GeodesicTrace whose geodesic status this certificate attests. Uses IRI string (cert cannot import trace).
geodesicTraceObjecttrueGeodesicCertificateGeodesicTraceThe computation trace that this GeodesicCertificate covers. Redundant with certifiedGeodesic but expresses the inverse direction for queryability.
certifiedMeasurementObjecttrueMeasurementCertificateMeasurementEventThe MeasurementEvent whose QM_1 compliance this certificate attests. Uses IRI string (cert cannot import trace).
vonNeumannEntropyDatatypetrueMeasurementCertificatedecimalThe von Neumann entropy S_vN of the pre-measurement SuperposedSiteState, recorded by this certificate.
landauerCostDatatypetrueMeasurementCertificatedecimalThe Landauer cost incurred by the projective collapse, recorded by this certificate. Equals vonNeumannEntropy at β* = ln 2 per QM_1.
evidenceBundleObjecttrueGeodesicCertificateGeodesicEvidenceBundleThe GeodesicEvidenceBundle attesting to the decomposed sub-predicates (isAR1Ordered, isDC10Selected) of this GeodesicCertificate's geodesic claim.
bornRuleVerifiedDatatypetrueBornRuleVerificationbooleanWhether this BornRuleVerification certificate confirms that all outcome probabilities match the Born rule (QM_5): P(k) = |α_k|² for every site k.
certifiedChainObjecttrueLiftChainCertificateLiftChainThe LiftChain this certificate attests to.
chainAuditTrailObjecttrueLiftChainCertificateChainAuditTrailThe ordered per-step evidence for this certificate.
targetLevelObjecttrueLiftChainCertificateWittLevelThe quantum level Q_k at which the certificate was issued.
sourceLevelObjecttrueLiftChainCertificateWittLevelThe quantum level Q_j from which the tower was started.
chainStepCountDatatypetrueChainAuditTrailnonNegativeIntegerNumber of lift steps in this ChainAuditTrail. Must equal chainLength of the certified LiftChain. Distinct from witnessCount (domain-locked to CompletenessAuditTrail).
isAR1OrderedDatatypetrueGeodesicEvidenceBundlebooleanTrue iff the linked GeodesicTrace is ordered by the AR_1 canonical rewriting rule (smallest lexicographic representative first).
isDC10SelectedDatatypetrueGeodesicEvidenceBundlebooleanTrue iff each constraint in the trace was selected by the DC_10 Jacobian oracle at the step where it was applied.
witnessObjectfalseInhabitanceCertificateValueTupleA specific value tuple in the carrier when verified is true; absent otherwise. The witness form for cert:InhabitanceCertificate.
searchTraceObjecttrueInhabitanceCertificateInhabitanceSearchTraceThe audit trail of the inhabitance search that produced this certificate.
groundedObjecttrueInhabitanceCertificateConstrainedTypeThe type:ConstrainedType this InhabitanceCertificate is issued for.
splittingFactorDatatypetrueMultiplicationCertificatepositiveIntegerThe 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.
subMultiplicationCountDatatypetrueMultiplicationCertificatenonNegativeIntegerThe 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.
landauerCostNatsDatatypetrueMultiplicationCertificatedecimalThe 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.