UOR Certificates
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
Imports
https://uor.foundation/op/https://uor.foundation/proof/https://uor.foundation/schema/https://uor.foundation/type/
Classes
| Name | Subclass Of | Disjoint With | Comment |
|---|---|---|---|
Certificate | Thing | A kernel-produced attestation. The root class for all certificate types. | |
TransformCertificate | Certificate | A certificate attesting to the properties of a morphism:Transform. Certifies that the transform maps source to target correctly. | |
IsometryCertificate | Certificate | A certificate attesting that a morphism:Isometry preserves metric distances. Certifies the transform is a metric isometry with respect to the specified metric. | |
InvolutionCertificate | Certificate | A certificate attesting that an operation is an involution: f(f(x)) = x for all x in R_n. | |
CompletenessCertificate | Certificate | A 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. | |
CompletenessAuditTrail | Thing | An ordered collection of CompletenessWitness records belonging to a CompletenessCertificate. Provides full provenance of the certification process: every constraint applied, every site closed, in sequence. | |
GroundingCertificate | Certificate | A 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. | |
GeodesicCertificate | Certificate | A certificate attesting that a trace:GeodesicTrace satisfies both GD_1 conditions: AR_1-ordered and DC_10-selected. Transforms ComputationTrace from descriptive to normative. | |
MeasurementCertificate | Certificate | A certificate attesting that a trace:MeasurementEvent respected the von Neumann–Landauer bridge (QM_1): preCollapseEntropy = postCollapseLandauerCost at β* = ln 2. | |
GeodesicEvidenceBundle | Thing | A structured evidence bundle attesting that each sub-predicate of the geodesic condition (GD_6) holds independently: isAR1Ordered and isDC10Selected. Linked from GeodesicCertificate via evidenceBundle. | |
BornRuleVerification | Certificate | A 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. | |
LiftChainCertificate | Certificate | A kernel-issued certificate attesting that a LiftChain from liftSourceLevel to liftTargetLevel is complete. | |
ChainAuditTrail | Thing | An ordered collection of per-step evidence records for a LiftChainCertificate. | |
InhabitanceCertificate | ComputationCertificate, Certificate | A 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. | |
MultiplicationCertificate | Certificate | A 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. | |
PartitionCertificate | Certificate | A 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. | |
GenericImpossibilityCertificate | Certificate | A 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. | |
InhabitanceImpossibilityCertificate | Certificate | A 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
| Name | Kind | Functional | Domain | Range | Comment |
|---|---|---|---|---|---|
transformType | Object | true | TransformCertificate | TermExpression | The type of transform this certificate attests to (e.g., 'isometry', 'embedding', 'action'). |
method | Object | true | Certificate | ProofStrategy | The verification method used to produce this certificate (e.g., 'exhaustive_check', 'symbolic_proof', 'sampling'). |
operation | Object | true | InvolutionCertificate | Operation | The operation this certificate applies to. |
verified | Datatype | true | Certificate | boolean | Whether this certificate has been verified by the kernel. |
wittLength | Datatype | true | Certificate | positiveInteger | The Witt level at which this certificate was produced. |
timestamp | Datatype | true | Certificate | dateTime | The time at which this certificate was issued. |
certifies | Object | true | Certificate | Thing | The resource this certificate attests to. Links a certificate to the observable, transform, or other entity it covers. |
certifiedType | Object | true | CompletenessCertificate | 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 | CompletenessCertificate | CompletenessAuditTrail | The audit trail attesting the certification provenance. Links a CompletenessCertificate to its ordered sequence of CompletenessWitness records. |
witnessCount | Datatype | true | CompletenessAuditTrail | nonNegativeInteger | Total number of witness steps in this audit trail. |
certifiedGrounding | Object | true | GroundingCertificate | GroundedContext | The GroundedContext whose full saturation this certificate attests. Uses IRI string (cert cannot import state). |
groundingWitness | Object | true | GroundingCertificate | GroundingWitness | The GroundingWitness providing step-by-step evidence of the saturation process. |
certifiedGeodesic | Object | true | GeodesicCertificate | GeodesicTrace | The GeodesicTrace whose geodesic status this certificate attests. Uses IRI string (cert cannot import trace). |
geodesicTrace | Object | true | GeodesicCertificate | GeodesicTrace | The computation trace that this GeodesicCertificate covers. Redundant with certifiedGeodesic but expresses the inverse direction for queryability. |
certifiedMeasurement | Object | true | MeasurementCertificate | MeasurementEvent | The MeasurementEvent whose QM_1 compliance this certificate attests. Uses IRI string (cert cannot import trace). |
vonNeumannEntropy | Datatype | true | MeasurementCertificate | decimal | The von Neumann entropy S_vN of the pre-measurement SuperposedSiteState, recorded by this certificate. |
landauerCost | Datatype | true | MeasurementCertificate | 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 | GeodesicCertificate | GeodesicEvidenceBundle | The GeodesicEvidenceBundle attesting to the decomposed sub-predicates (isAR1Ordered, isDC10Selected) of this GeodesicCertificate's geodesic claim. |
bornRuleVerified | Datatype | true | BornRuleVerification | 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 | LiftChainCertificate | LiftChain | The LiftChain this certificate attests to. |
chainAuditTrail | Object | true | LiftChainCertificate | ChainAuditTrail | The ordered per-step evidence for this certificate. |
targetLevel | Object | true | LiftChainCertificate | WittLevel | The quantum level Q_k at which the certificate was issued. |
sourceLevel | Object | true | LiftChainCertificate | WittLevel | The quantum level Q_j from which the tower was started. |
chainStepCount | Datatype | true | ChainAuditTrail | 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 | GeodesicEvidenceBundle | boolean | True iff the linked GeodesicTrace is ordered by the AR_1 canonical rewriting rule (smallest lexicographic representative first). |
isDC10Selected | Datatype | true | GeodesicEvidenceBundle | boolean | True iff each constraint in the trace was selected by the DC_10 Jacobian oracle at the step where it was applied. |
witness | Object | false | InhabitanceCertificate | ValueTuple | A specific value tuple in the carrier when verified is true; absent otherwise. The witness form for cert:InhabitanceCertificate. |
searchTrace | Object | true | InhabitanceCertificate | InhabitanceSearchTrace | The audit trail of the inhabitance search that produced this certificate. |
grounded | Object | true | InhabitanceCertificate | ConstrainedType | The type:ConstrainedType this InhabitanceCertificate is issued for. |
splittingFactor | Datatype | true | MultiplicationCertificate | positiveInteger | The 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. |
subMultiplicationCount | Datatype | true | MultiplicationCertificate | nonNegativeInteger | The 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. |
landauerCostNats | Datatype | true | MultiplicationCertificate | decimal | The 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. |