| transformType | Object | true | https://uor.foundation/cert/TransformCertificate | https://uor.foundation/schema/TermExpression | The type of transform this certificate attests to (e.g., 'isometry', 'embedding', 'action'). |
| method | Object | true | https://uor.foundation/cert/Certificate | https://uor.foundation/proof/ProofStrategy | The verification method used to produce this certificate (e.g., 'exhaustive_check', 'symbolic_proof', 'sampling'). |
| operation | Object | true | https://uor.foundation/cert/InvolutionCertificate | https://uor.foundation/op/Operation | The operation this certificate applies to. |
| verified | Datatype | true | https://uor.foundation/cert/Certificate | http://www.w3.org/2001/XMLSchema#boolean | Whether this certificate has been verified by the kernel. |
| wittLength | Datatype | true | https://uor.foundation/cert/Certificate | http://www.w3.org/2001/XMLSchema#positiveInteger | The Witt level at which this certificate was produced. |
| timestamp | Datatype | true | https://uor.foundation/cert/Certificate | http://www.w3.org/2001/XMLSchema#dateTime | The time at which this certificate was issued. |
| certifies | Object | true | https://uor.foundation/cert/Certificate | http://www.w3.org/2002/07/owl#Thing | The resource this certificate attests to. Links a certificate to the observable, transform, or other entity it covers. |
| certifiedType | Object | true | https://uor.foundation/cert/CompletenessCertificate | https://uor.foundation/type/CompleteType | The 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. |
| auditTrail | Object | true | https://uor.foundation/cert/CompletenessCertificate | https://uor.foundation/cert/CompletenessAuditTrail | The audit trail attesting the certification provenance. Links a CompletenessCertificate to its ordered sequence of CompletenessWitness records. |
| witnessCount | Datatype | true | https://uor.foundation/cert/CompletenessAuditTrail | http://www.w3.org/2001/XMLSchema#nonNegativeInteger | Total number of witness steps in this audit trail. |
| certifiedGrounding | Object | true | https://uor.foundation/cert/GroundingCertificate | https://uor.foundation/state/GroundedContext | The GroundedContext whose full saturation this certificate attests. Uses IRI string (cert cannot import state). |
| groundingWitness | Object | true | https://uor.foundation/cert/GroundingCertificate | https://uor.foundation/state/GroundingWitness | The GroundingWitness providing step-by-step evidence of the saturation process. |
| certifiedGeodesic | Object | true | https://uor.foundation/cert/GeodesicCertificate | https://uor.foundation/trace/GeodesicTrace | The GeodesicTrace whose geodesic status this certificate attests. Uses IRI string (cert cannot import trace). |
| geodesicTrace | Object | true | https://uor.foundation/cert/GeodesicCertificate | https://uor.foundation/trace/GeodesicTrace | The computation trace that this GeodesicCertificate covers. Redundant with certifiedGeodesic but expresses the inverse direction for queryability. |
| certifiedMeasurement | Object | true | https://uor.foundation/cert/MeasurementCertificate | https://uor.foundation/trace/MeasurementEvent | The MeasurementEvent whose QM_1 compliance this certificate attests. Uses IRI string (cert cannot import trace). |
| vonNeumannEntropy | Datatype | true | https://uor.foundation/cert/MeasurementCertificate | http://www.w3.org/2001/XMLSchema#decimal | The von Neumann entropy S_vN of the pre-measurement SuperposedSiteState, recorded by this certificate. |
| landauerCost | Datatype | true | https://uor.foundation/cert/MeasurementCertificate | http://www.w3.org/2001/XMLSchema#decimal | The Landauer cost incurred by the projective collapse, recorded by this certificate. Equals vonNeumannEntropy at β* = ln 2 per QM_1. |
| evidenceBundle | Object | true | https://uor.foundation/cert/GeodesicCertificate | https://uor.foundation/cert/GeodesicEvidenceBundle | The GeodesicEvidenceBundle attesting to the decomposed sub-predicates (isAR1Ordered, isDC10Selected) of this GeodesicCertificate's geodesic claim. |
| bornRuleVerified | Datatype | true | https://uor.foundation/cert/BornRuleVerification | http://www.w3.org/2001/XMLSchema#boolean | Whether this BornRuleVerification certificate confirms that all outcome probabilities match the Born rule (QM_5): P(k) = |α_k|² for every site k. |
| certifiedChain | Object | true | https://uor.foundation/cert/LiftChainCertificate | https://uor.foundation/type/LiftChain | The LiftChain this certificate attests to. |
| chainAuditTrail | Object | true | https://uor.foundation/cert/LiftChainCertificate | https://uor.foundation/cert/ChainAuditTrail | The ordered per-step evidence for this certificate. |
| targetLevel | Object | true | https://uor.foundation/cert/LiftChainCertificate | https://uor.foundation/schema/WittLevel | The quantum level Q_k at which the certificate was issued. |
| sourceLevel | Object | true | https://uor.foundation/cert/LiftChainCertificate | https://uor.foundation/schema/WittLevel | The quantum level Q_j from which the tower was started. |
| chainStepCount | Datatype | true | https://uor.foundation/cert/ChainAuditTrail | http://www.w3.org/2001/XMLSchema#nonNegativeInteger | Number of lift steps in this ChainAuditTrail. Must equal chainLength of the certified LiftChain. Distinct from witnessCount (domain-locked to CompletenessAuditTrail). |
| isAR1Ordered | Datatype | true | https://uor.foundation/cert/GeodesicEvidenceBundle | http://www.w3.org/2001/XMLSchema#boolean | True iff the linked GeodesicTrace is ordered by the AR_1 canonical rewriting rule (smallest lexicographic representative first). |
| isDC10Selected | Datatype | true | https://uor.foundation/cert/GeodesicEvidenceBundle | http://www.w3.org/2001/XMLSchema#boolean | True iff each constraint in the trace was selected by the DC_10 Jacobian oracle at the step where it was applied. |