| quantum | Datatype | true | https://uor.foundation/proof/Proof | http://www.w3.org/2001/XMLSchema#positiveInteger | The quantum level at which this proof was verified. |
| verified | Datatype | true | https://uor.foundation/proof/Proof | http://www.w3.org/2001/XMLSchema#boolean | Whether this proof has been verified by the kernel. |
| timestamp | Datatype | true | https://uor.foundation/proof/Proof | http://www.w3.org/2001/XMLSchema#dateTime | The time at which this proof was produced. |
| witness | Object | false | https://uor.foundation/proof/Proof | https://uor.foundation/proof/WitnessData | Supporting witness data for this proof. |
| criticalIdentity | Datatype | true | https://uor.foundation/proof/CriticalIdentityProof | http://www.w3.org/2001/XMLSchema#string | Human-readable statement of the critical identity proven. E.g., 'neg(bnot(x)) = succ(x) for all x in R_n'. |
| x | Datatype | false | https://uor.foundation/proof/WitnessData | http://www.w3.org/2001/XMLSchema#integer | A specific input value used as a witness for the critical identity check. |
| bnot_x | Datatype | false | https://uor.foundation/proof/WitnessData | http://www.w3.org/2001/XMLSchema#integer | The value bnot(x) for a witness x. |
| neg_bnot_x | Datatype | false | https://uor.foundation/proof/WitnessData | http://www.w3.org/2001/XMLSchema#integer | The value neg(bnot(x)) for a witness x. |
| succ_x | Datatype | false | https://uor.foundation/proof/WitnessData | http://www.w3.org/2001/XMLSchema#integer | The value succ(x) for a witness x. |
| holds | Datatype | false | https://uor.foundation/proof/WitnessData | http://www.w3.org/2001/XMLSchema#boolean | Whether the identity neg(bnot(x)) = succ(x) holds for this specific witness. |
| provesIdentity | Object | true | https://uor.foundation/proof/Proof | https://uor.foundation/op/Identity | The algebraic identity this proof establishes. Provides a canonical object reference alongside the existing proof:criticalIdentity string property, which remains for human readability. |