UOR Proofs

IRI: https://uor.foundation/proof/
Prefix: proof:
Space: bridge
Comment: Kernel-produced verification proofs attesting to algebraic properties of UOR objects and operations.

Imports

Name	Subclass Of	Comment
`Proof`	`Thing`	A kernel-produced attestation that a given algebraic property holds. The root class for all proof types.
`CoherenceProof`	`Proof`	A proof of coherence: the type system and ring structure are mutually consistent at a given quantum level.
`CriticalIdentityProof`	`Proof`	A proof of the critical identity: neg(bnot(x)) = succ(x) for all x in R_n. This is the foundational theorem of the UOR kernel.
`WitnessData`	`Thing`	Supporting data for a proof: specific examples, counter-examples checked, or intermediate computation results.

Name	Kind	Functional	Domain	Range	Comment
`quantum`	Datatype	true	`Proof`	`positiveInteger`	The quantum level at which this proof was verified.
`verified`	Datatype	true	`Proof`	`boolean`	Whether this proof has been verified by the kernel.
`timestamp`	Datatype	true	`Proof`	`dateTime`	The time at which this proof was produced.
`witness`	Object	false	`Proof`	`WitnessData`	Supporting witness data for this proof.
`criticalIdentity`	Datatype	true	`CriticalIdentityProof`	`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	`WitnessData`	`integer`	A specific input value used as a witness for the critical identity check.
`bnot_x`	Datatype	false	`WitnessData`	`integer`	The value bnot(x) for a witness x.
`neg_bnot_x`	Datatype	false	`WitnessData`	`integer`	The value neg(bnot(x)) for a witness x.
`succ_x`	Datatype	false	`WitnessData`	`integer`	The value succ(x) for a witness x.
`holds`	Datatype	false	`WitnessData`	`boolean`	Whether the identity neg(bnot(x)) = succ(x) holds for this specific witness.
`provesIdentity`	Object	true	`Proof`	`Identity`	The algebraic identity this proof establishes. Provides a canonical object reference alongside the existing proof:criticalIdentity string property, which remains for human readability.