uor-foundation 0.3.2

// @generated by uor-crate from uor-ontology — do not edit manually

//! `proof/` namespace — Kernel-produced verification proofs attesting to algebraic properties of UOR objects and operations..
//!
//! Space: Bridge

use crate::enums::AchievabilityStatus;
use crate::enums::ProofStrategy;
use crate::enums::VerificationDomain;
use crate::enums::WittLevel;
use crate::HostTypes;

/// A kernel-produced attestation that a given algebraic property holds. The root class for all proof types.
pub trait Proof<H: HostTypes> {
    /// Whether this proof has been verified by the kernel.
    fn verified(&self) -> bool;
    /// The time at which this proof was produced.
    fn timestamp(&self) -> &H::WitnessBytes;
    /// Associated type for `WitnessData`.
    type WitnessData: WitnessData<H>;
    /// Supporting witness data for this proof.
    fn witness(&self) -> &[Self::WitnessData];
    /// Associated type for `Identity`.
    type Identity: crate::kernel::op::Identity<H>;
    /// The algebraic identity this proof establishes. Provides a canonical object reference alongside the existing proof:criticalIdentity string property, which remains for human readability.
    fn proves_identity(&self) -> &Self::Identity;
    /// The specific quantum level at which an empirical verification or impossibility witness was established.
    fn verified_at_level(&self) -> &[WittLevel];
    /// The proof method from the ProofStrategy controlled vocabulary. Determines the compilation target (e.g., `by ring`, `by simp`, `by induction`).
    fn strategy(&self) -> ProofStrategy;
    /// An identity that this proof depends on as a lemma. Forms the proof dependency DAG. Leaf proofs (provable from definitions alone) have no dependsOn assertions.
    fn depends_on(&self) -> &[Self::Identity];
    /// Associated type for `DerivationTerm`.
    type DerivationTerm: DerivationTerm<H>;
    /// The formal proof construction term: a DerivationTerm AST node encoding the tactic script, lemma chain, or induction scaffold that constitutes the proof.
    fn formal_derivation(&self) -> &Self::DerivationTerm;
}

/// A proof of coherence: the type system and ring structure are mutually consistent at a given quantum level.
pub trait CoherenceProof<H: HostTypes>: Proof<H> {}

/// A proof confirmed by exhaustive execution over R_n at a specific quantum level. The kernel ran the identity against all 2^n inputs and observed that it holds. The proof:atWittLevel property records the level; proof:witness links to the WitnessData. CriticalIdentityProof is a subclass of ComputationCertificate.
pub trait ComputationCertificate<H: HostTypes>: Proof<H> {
    /// The quantum level at which this computation certificate was produced. A ComputationCertificate at schema:Q0 confirms the identity holds for all 256 inputs of R_8. A certificate at schema:Q1 confirms it for all 65,536 inputs of R_16.
    fn at_witt_level(&self) -> WittLevel;
}

/// A proof that follows from previously established axioms or definitions by equational, structural, or topological reasoning. The proof:derivationWitness property links to a derivation:Derivation individual recording the rewrite chain. All pipeline, constraint, observable, and topological identities are AxiomaticDerivations.
pub trait AxiomaticDerivation<H: HostTypes>: Proof<H> {
    /// True when this axiomatic derivation holds for all quantum levels by the definition of Z/(2^n)Z. False when the derivation depends on a property specific to a particular ring size. All current AxiomaticDerivation individuals in the spec carry universalScope true.
    fn universal_scope(&self) -> bool;
    /// Associated type for `Derivation`.
    type Derivation: crate::bridge::derivation::Derivation<H>;
    /// The derivation chain that witnesses this axiomatic derivation. Links a proof:AxiomaticDerivation to the derivation:Derivation individual recording the rewrite sequence. Optional at the spec level — the conformance suite requires only that the proof individual exists; full derivation chains live in generated artifacts.
    fn derivation_witness(&self) -> &[Self::Derivation];
}

/// 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.
pub trait CriticalIdentityProof<H: HostTypes>: ComputationCertificate<H> {}

/// Supporting data for a proof: specific examples, counter-examples checked, or intermediate computation results.
pub trait WitnessData<H: HostTypes> {
    /// A specific input value used as a witness for the critical identity check.
    fn x(&self) -> &[i64];
    /// The value bnot(x) for a witness x.
    fn bnot_x(&self) -> &[i64];
    /// The value neg(bnot(x)) for a witness x.
    fn neg_bnot_x(&self) -> &[i64];
    /// The value succ(x) for a witness x.
    fn succ_x(&self) -> &[i64];
    /// Whether the identity neg(bnot(x)) = succ(x) holds for this specific witness.
    fn holds(&self) -> &[bool];
}

/// A formal witness that a topological signature (χ, β_k) is impossible to achieve for any ConstrainedType. Carries the algebraic reason and the verification domain grounding the impossibility.
pub trait ImpossibilityWitness<H: HostTypes>: Proof<H> {
    /// Human-readable statement of the algebraic reason the signature is impossible (e.g., 'β₀ = 0 violates MS_1').
    fn impossibility_reason(&self) -> &H::HostString;
    /// The verification domain grounding the impossibility (e.g., Pipeline for β₀ = 0, Algebraic for χ > n).
    fn impossibility_domain(&self) -> VerificationDomain;
    /// The achievability classification of a proof-linked observable signature: Achievable or Forbidden.
    fn achievability_status(&self) -> AchievabilityStatus;
}

/// A formal record of a morphospace boundary point — either an achievable or forbidden topological signature. Aggregated by MorphospaceBoundary to form the queryable morphospace map.
pub trait MorphospaceRecord<H: HostTypes> {
    /// Whether this MorphospaceRecord represents an impossibility boundary (from below) or an achievability boundary (from above).
    fn boundary_type(&self) -> AchievabilityStatus;
}

/// An aggregate of ImpossibilityWitness instances forming the queryable morphospace map. SPARQL over this structure answers achievability queries in O(1).
pub trait MorphospaceBoundary<H: HostTypes> {
    /// Associated type for `MorphospaceRecord`.
    type MorphospaceRecord: MorphospaceRecord<H>;
    /// Links a MorphospaceBoundary to one of its constituent MorphospaceRecord individuals.
    fn morphospace_record(&self) -> &[Self::MorphospaceRecord];
}

/// A proof by structural induction on the quantum level index k. Carries a base case proof, an inductive step proof, and the minimum k for which the induction holds.
pub trait InductiveProof<H: HostTypes>: Proof<H> {
    /// Associated type for `Proof`.
    type Proof: Proof<H>;
    /// The proof that the claim holds at the base level k_0.
    fn base_case(&self) -> &Self::Proof;
    /// The proof that if the claim holds at Q_k, it holds at Q_{k+1}.
    fn inductive_step(&self) -> &Self::Proof;
    /// The minimum k for which the induction is valid.
    fn valid_for_kat_least(&self) -> u64;
}

/// Root AST node for proof construction terms. Distinct from schema:TermExpression which represents mathematical terms; DerivationTerm represents proof constructions (tactic applications, lemma invocations, induction scaffolding).
pub trait DerivationTerm<H: HostTypes> {}

/// A proof step applying a named tactic (from ProofStrategy) with arguments. Maps to a Lean4 tactic invocation.
pub trait TacticApplication<H: HostTypes>: DerivationTerm<H> {}

/// A proof step invoking a previously proved identity as a lemma. References the identity via proof:dependsOn.
pub trait LemmaInvocation<H: HostTypes>: DerivationTerm<H> {}

/// A proof step performing structural induction: base case derivation, inductive hypothesis, and step derivation.
pub trait InductionStep<H: HostTypes>: DerivationTerm<H> {}

/// A proof step performing exhaustive computation at a specific quantum level as verification witness.
pub trait ComputationStep<H: HostTypes>: DerivationTerm<H> {}

/// A specialisation of proof:ImpossibilityWitness produced when the inhabitance search determines that the carrier of a ConstrainedType is empty. Aggregates into the existing proof:MorphospaceBoundary alongside other impossibility witnesses, inheriting its O(1) amortised lookup discipline for previously resolved signatures.
pub trait InhabitanceImpossibilityWitness<H: HostTypes>: ImpossibilityWitness<H> {
    /// The Lean 4 by-contradiction derivation over the predicate vocabulary attesting that no value tuple satisfies the constraint system.
    fn contradiction_proof(&self) -> &H::HostString;
    /// Associated type for `ConstrainedType`.
    type ConstrainedType: crate::user::type_::ConstrainedType<H>;
    /// The type:ConstrainedType whose carrier this witness certifies as empty.
    fn grounded(&self) -> &Self::ConstrainedType;
    /// Associated type for `InhabitanceSearchTrace`.
    type InhabitanceSearchTrace: crate::bridge::trace::InhabitanceSearchTrace<H>;
    /// The audit trail of the inhabitance search up to the contradiction.
    fn search_trace(&self) -> &Self::InhabitanceSearchTrace;
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `Proof<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullProof<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullProof<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullProof<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullProof<H> = NullProof {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Proof<H> for NullProof<H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `CoherenceProof<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullCoherenceProof<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullCoherenceProof<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullCoherenceProof<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullCoherenceProof<H> = NullCoherenceProof {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Proof<H> for NullCoherenceProof<H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<H: HostTypes> CoherenceProof<H> for NullCoherenceProof<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `ComputationCertificate<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullComputationCertificate<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullComputationCertificate<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullComputationCertificate<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullComputationCertificate<H> = NullComputationCertificate {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Proof<H> for NullComputationCertificate<H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<H: HostTypes> ComputationCertificate<H> for NullComputationCertificate<H> {
    fn at_witt_level(&self) -> WittLevel {
        <WittLevel>::default()
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `AxiomaticDerivation<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullAxiomaticDerivation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullAxiomaticDerivation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullAxiomaticDerivation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullAxiomaticDerivation<H> = NullAxiomaticDerivation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Proof<H> for NullAxiomaticDerivation<H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<H: HostTypes> AxiomaticDerivation<H> for NullAxiomaticDerivation<H> {
    fn universal_scope(&self) -> bool {
        false
    }
    type Derivation = crate::bridge::derivation::NullDerivation<H>;
    fn derivation_witness(&self) -> &[Self::Derivation] {
        &[]
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `CriticalIdentityProof<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullCriticalIdentityProof<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullCriticalIdentityProof<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullCriticalIdentityProof<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullCriticalIdentityProof<H> = NullCriticalIdentityProof {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Proof<H> for NullCriticalIdentityProof<H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<H: HostTypes> ComputationCertificate<H> for NullCriticalIdentityProof<H> {
    fn at_witt_level(&self) -> WittLevel {
        <WittLevel>::default()
    }
}
impl<H: HostTypes> CriticalIdentityProof<H> for NullCriticalIdentityProof<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `WitnessData<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullWitnessData<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullWitnessData<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullWitnessData<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullWitnessData<H> = NullWitnessData {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> WitnessData<H> for NullWitnessData<H> {
    fn x(&self) -> &[i64] {
        &[]
    }
    fn bnot_x(&self) -> &[i64] {
        &[]
    }
    fn neg_bnot_x(&self) -> &[i64] {
        &[]
    }
    fn succ_x(&self) -> &[i64] {
        &[]
    }
    fn holds(&self) -> &[bool] {
        &[]
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `ImpossibilityWitness<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullImpossibilityWitness<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullImpossibilityWitness<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullImpossibilityWitness<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullImpossibilityWitness<H> = NullImpossibilityWitness {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Proof<H> for NullImpossibilityWitness<H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<H: HostTypes> ImpossibilityWitness<H> for NullImpossibilityWitness<H> {
    fn impossibility_reason(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn impossibility_domain(&self) -> VerificationDomain {
        <VerificationDomain>::default()
    }
    fn achievability_status(&self) -> AchievabilityStatus {
        <AchievabilityStatus>::default()
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `MorphospaceRecord<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullMorphospaceRecord<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullMorphospaceRecord<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullMorphospaceRecord<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullMorphospaceRecord<H> = NullMorphospaceRecord {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> MorphospaceRecord<H> for NullMorphospaceRecord<H> {
    fn boundary_type(&self) -> AchievabilityStatus {
        <AchievabilityStatus>::default()
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `MorphospaceBoundary<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullMorphospaceBoundary<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullMorphospaceBoundary<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullMorphospaceBoundary<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullMorphospaceBoundary<H> = NullMorphospaceBoundary {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> MorphospaceBoundary<H> for NullMorphospaceBoundary<H> {
    type MorphospaceRecord = NullMorphospaceRecord<H>;
    fn morphospace_record(&self) -> &[Self::MorphospaceRecord] {
        &[]
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `InductiveProof<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullInductiveProof<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullInductiveProof<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullInductiveProof<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullInductiveProof<H> = NullInductiveProof {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Proof<H> for NullInductiveProof<H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<H: HostTypes> InductiveProof<H> for NullInductiveProof<H> {
    type Proof = NullProof<H>;
    fn base_case(&self) -> &Self::Proof {
        &<NullProof<H>>::ABSENT
    }
    fn inductive_step(&self) -> &Self::Proof {
        &<NullProof<H>>::ABSENT
    }
    fn valid_for_kat_least(&self) -> u64 {
        0
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `DerivationTerm<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullDerivationTerm<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullDerivationTerm<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullDerivationTerm<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullDerivationTerm<H> = NullDerivationTerm {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> DerivationTerm<H> for NullDerivationTerm<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `TacticApplication<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullTacticApplication<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullTacticApplication<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullTacticApplication<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullTacticApplication<H> = NullTacticApplication {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> DerivationTerm<H> for NullTacticApplication<H> {}
impl<H: HostTypes> TacticApplication<H> for NullTacticApplication<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `LemmaInvocation<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullLemmaInvocation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullLemmaInvocation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullLemmaInvocation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullLemmaInvocation<H> = NullLemmaInvocation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> DerivationTerm<H> for NullLemmaInvocation<H> {}
impl<H: HostTypes> LemmaInvocation<H> for NullLemmaInvocation<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `InductionStep<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullInductionStep<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullInductionStep<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullInductionStep<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullInductionStep<H> = NullInductionStep {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> DerivationTerm<H> for NullInductionStep<H> {}
impl<H: HostTypes> InductionStep<H> for NullInductionStep<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `ComputationStep<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullComputationStep<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullComputationStep<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullComputationStep<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullComputationStep<H> = NullComputationStep {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> DerivationTerm<H> for NullComputationStep<H> {}
impl<H: HostTypes> ComputationStep<H> for NullComputationStep<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `InhabitanceImpossibilityWitness<H>`.
/// Every accessor returns `H::EMPTY_*` sentinels (for scalar / host-typed
/// returns) or a `'static`-lifetime reference to a sibling `Null*`'s `ABSENT`
/// const (for trait-typed returns).  Downstream provides concrete impls;
/// this stub closes the ontology-derived trait orphan.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub struct NullInhabitanceImpossibilityWitness<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullInhabitanceImpossibilityWitness<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullInhabitanceImpossibilityWitness<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullInhabitanceImpossibilityWitness<H> =
        NullInhabitanceImpossibilityWitness {
            _phantom: core::marker::PhantomData,
        };
}
impl<H: HostTypes> Proof<H> for NullInhabitanceImpossibilityWitness<H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<H: HostTypes> ImpossibilityWitness<H> for NullInhabitanceImpossibilityWitness<H> {
    fn impossibility_reason(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn impossibility_domain(&self) -> VerificationDomain {
        <VerificationDomain>::default()
    }
    fn achievability_status(&self) -> AchievabilityStatus {
        <AchievabilityStatus>::default()
    }
}
impl<H: HostTypes> InhabitanceImpossibilityWitness<H> for NullInhabitanceImpossibilityWitness<H> {
    fn contradiction_proof(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ConstrainedType = crate::user::type_::NullConstrainedType<H>;
    fn grounded(&self) -> &Self::ConstrainedType {
        &<crate::user::type_::NullConstrainedType<H>>::ABSENT
    }
    type InhabitanceSearchTrace = crate::bridge::trace::NullInhabitanceSearchTrace<H>;
    fn search_trace(&self) -> &Self::InhabitanceSearchTrace {
        &<crate::bridge::trace::NullInhabitanceSearchTrace<H>>::ABSENT
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `Proof<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct ProofHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for ProofHandle<H> {}
impl<H: HostTypes> Clone for ProofHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for ProofHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for ProofHandle<H> {}
impl<H: HostTypes> core::hash::Hash for ProofHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> ProofHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `Proof<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait ProofResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: ProofHandle<H>) -> Option<ProofRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `Proof<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct ProofRecord<H: HostTypes> {
    pub verified: bool,
    pub timestamp: &'static H::WitnessBytes,
    pub proves_identity_handle: crate::kernel::op::IdentityHandle<H>,
    pub strategy: ProofStrategy,
    pub formal_derivation_handle: DerivationTermHandle<H>,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `Proof<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedProof<'r, R: ProofResolver<H>, H: HostTypes> {
    handle: ProofHandle<H>,
    resolver: &'r R,
    record: Option<ProofRecord<H>>,
}
impl<'r, R: ProofResolver<H>, H: HostTypes> ResolvedProof<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: ProofHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> ProofHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&ProofRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: ProofResolver<H>, H: HostTypes> Proof<H> for ResolvedProof<'r, R, H> {
    fn verified(&self) -> bool {
        match &self.record {
            Some(r) => r.verified,
            None => false,
        }
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        match &self.record {
            Some(r) => r.timestamp,
            None => H::EMPTY_WITNESS_BYTES,
        }
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        match &self.record {
            Some(r) => r.strategy,
            None => <ProofStrategy>::default(),
        }
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<'r, R: ProofResolver<H>, H: HostTypes> ResolvedProof<'r, R, H> {
    /// Promote the `proves_identity` handle on the cached record into a
    /// resolved wrapper, given a resolver for the range class.
    /// Returns `None` if no record was resolved at construction.
    #[inline]
    pub fn resolve_proves_identity<'r2, R2: crate::kernel::op::IdentityResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::kernel::op::ResolvedIdentity<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::kernel::op::ResolvedIdentity::new(
            record.proves_identity_handle,
            r,
        ))
    }
    /// Promote the `formal_derivation` handle on the cached record into a
    /// resolved wrapper, given a resolver for the range class.
    /// Returns `None` if no record was resolved at construction.
    #[inline]
    pub fn resolve_formal_derivation<'r2, R2: DerivationTermResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedDerivationTerm<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedDerivationTerm::new(
            record.formal_derivation_handle,
            r,
        ))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `CoherenceProof<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct CoherenceProofHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for CoherenceProofHandle<H> {}
impl<H: HostTypes> Clone for CoherenceProofHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for CoherenceProofHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for CoherenceProofHandle<H> {}
impl<H: HostTypes> core::hash::Hash for CoherenceProofHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> CoherenceProofHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `CoherenceProof<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait CoherenceProofResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: CoherenceProofHandle<H>) -> Option<CoherenceProofRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `CoherenceProof<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct CoherenceProofRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `CoherenceProof<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedCoherenceProof<'r, R: CoherenceProofResolver<H>, H: HostTypes> {
    handle: CoherenceProofHandle<H>,
    resolver: &'r R,
    record: Option<CoherenceProofRecord<H>>,
}
impl<'r, R: CoherenceProofResolver<H>, H: HostTypes> ResolvedCoherenceProof<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: CoherenceProofHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> CoherenceProofHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&CoherenceProofRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: CoherenceProofResolver<H>, H: HostTypes> Proof<H> for ResolvedCoherenceProof<'r, R, H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<'r, R: CoherenceProofResolver<H>, H: HostTypes> CoherenceProof<H>
    for ResolvedCoherenceProof<'r, R, H>
{
}

/// Phase 8 (orphan-closure) — content-addressed handle for `ComputationCertificate<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct ComputationCertificateHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for ComputationCertificateHandle<H> {}
impl<H: HostTypes> Clone for ComputationCertificateHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for ComputationCertificateHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for ComputationCertificateHandle<H> {}
impl<H: HostTypes> core::hash::Hash for ComputationCertificateHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> ComputationCertificateHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `ComputationCertificate<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait ComputationCertificateResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(
        &self,
        handle: ComputationCertificateHandle<H>,
    ) -> Option<ComputationCertificateRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `ComputationCertificate<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct ComputationCertificateRecord<H: HostTypes> {
    pub at_witt_level: WittLevel,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `ComputationCertificate<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedComputationCertificate<'r, R: ComputationCertificateResolver<H>, H: HostTypes> {
    handle: ComputationCertificateHandle<H>,
    resolver: &'r R,
    record: Option<ComputationCertificateRecord<H>>,
}
impl<'r, R: ComputationCertificateResolver<H>, H: HostTypes>
    ResolvedComputationCertificate<'r, R, H>
{
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: ComputationCertificateHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> ComputationCertificateHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&ComputationCertificateRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: ComputationCertificateResolver<H>, H: HostTypes> Proof<H>
    for ResolvedComputationCertificate<'r, R, H>
{
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<'r, R: ComputationCertificateResolver<H>, H: HostTypes> ComputationCertificate<H>
    for ResolvedComputationCertificate<'r, R, H>
{
    fn at_witt_level(&self) -> WittLevel {
        match &self.record {
            Some(r) => r.at_witt_level,
            None => <WittLevel>::default(),
        }
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `AxiomaticDerivation<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct AxiomaticDerivationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for AxiomaticDerivationHandle<H> {}
impl<H: HostTypes> Clone for AxiomaticDerivationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for AxiomaticDerivationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for AxiomaticDerivationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for AxiomaticDerivationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> AxiomaticDerivationHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `AxiomaticDerivation<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait AxiomaticDerivationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: AxiomaticDerivationHandle<H>)
        -> Option<AxiomaticDerivationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `AxiomaticDerivation<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct AxiomaticDerivationRecord<H: HostTypes> {
    pub universal_scope: bool,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `AxiomaticDerivation<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedAxiomaticDerivation<'r, R: AxiomaticDerivationResolver<H>, H: HostTypes> {
    handle: AxiomaticDerivationHandle<H>,
    resolver: &'r R,
    record: Option<AxiomaticDerivationRecord<H>>,
}
impl<'r, R: AxiomaticDerivationResolver<H>, H: HostTypes> ResolvedAxiomaticDerivation<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: AxiomaticDerivationHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> AxiomaticDerivationHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&AxiomaticDerivationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: AxiomaticDerivationResolver<H>, H: HostTypes> Proof<H>
    for ResolvedAxiomaticDerivation<'r, R, H>
{
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<'r, R: AxiomaticDerivationResolver<H>, H: HostTypes> AxiomaticDerivation<H>
    for ResolvedAxiomaticDerivation<'r, R, H>
{
    fn universal_scope(&self) -> bool {
        match &self.record {
            Some(r) => r.universal_scope,
            None => false,
        }
    }
    type Derivation = crate::bridge::derivation::NullDerivation<H>;
    fn derivation_witness(&self) -> &[Self::Derivation] {
        &[]
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `CriticalIdentityProof<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct CriticalIdentityProofHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for CriticalIdentityProofHandle<H> {}
impl<H: HostTypes> Clone for CriticalIdentityProofHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for CriticalIdentityProofHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for CriticalIdentityProofHandle<H> {}
impl<H: HostTypes> core::hash::Hash for CriticalIdentityProofHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> CriticalIdentityProofHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `CriticalIdentityProof<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait CriticalIdentityProofResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(
        &self,
        handle: CriticalIdentityProofHandle<H>,
    ) -> Option<CriticalIdentityProofRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `CriticalIdentityProof<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct CriticalIdentityProofRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `CriticalIdentityProof<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedCriticalIdentityProof<'r, R: CriticalIdentityProofResolver<H>, H: HostTypes> {
    handle: CriticalIdentityProofHandle<H>,
    resolver: &'r R,
    record: Option<CriticalIdentityProofRecord<H>>,
}
impl<'r, R: CriticalIdentityProofResolver<H>, H: HostTypes>
    ResolvedCriticalIdentityProof<'r, R, H>
{
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: CriticalIdentityProofHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> CriticalIdentityProofHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&CriticalIdentityProofRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: CriticalIdentityProofResolver<H>, H: HostTypes> Proof<H>
    for ResolvedCriticalIdentityProof<'r, R, H>
{
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<'r, R: CriticalIdentityProofResolver<H>, H: HostTypes> ComputationCertificate<H>
    for ResolvedCriticalIdentityProof<'r, R, H>
{
    fn at_witt_level(&self) -> WittLevel {
        <WittLevel>::default()
    }
}
impl<'r, R: CriticalIdentityProofResolver<H>, H: HostTypes> CriticalIdentityProof<H>
    for ResolvedCriticalIdentityProof<'r, R, H>
{
}

/// Phase 8 (orphan-closure) — content-addressed handle for `WitnessData<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct WitnessDataHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for WitnessDataHandle<H> {}
impl<H: HostTypes> Clone for WitnessDataHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for WitnessDataHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for WitnessDataHandle<H> {}
impl<H: HostTypes> core::hash::Hash for WitnessDataHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> WitnessDataHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `WitnessData<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait WitnessDataResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: WitnessDataHandle<H>) -> Option<WitnessDataRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `WitnessData<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct WitnessDataRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `WitnessData<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedWitnessData<'r, R: WitnessDataResolver<H>, H: HostTypes> {
    handle: WitnessDataHandle<H>,
    resolver: &'r R,
    record: Option<WitnessDataRecord<H>>,
}
impl<'r, R: WitnessDataResolver<H>, H: HostTypes> ResolvedWitnessData<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: WitnessDataHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> WitnessDataHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&WitnessDataRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: WitnessDataResolver<H>, H: HostTypes> WitnessData<H> for ResolvedWitnessData<'r, R, H> {
    fn x(&self) -> &[i64] {
        &[]
    }
    fn bnot_x(&self) -> &[i64] {
        &[]
    }
    fn neg_bnot_x(&self) -> &[i64] {
        &[]
    }
    fn succ_x(&self) -> &[i64] {
        &[]
    }
    fn holds(&self) -> &[bool] {
        &[]
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `MorphospaceRecord<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct MorphospaceRecordHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for MorphospaceRecordHandle<H> {}
impl<H: HostTypes> Clone for MorphospaceRecordHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for MorphospaceRecordHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for MorphospaceRecordHandle<H> {}
impl<H: HostTypes> core::hash::Hash for MorphospaceRecordHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> MorphospaceRecordHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `MorphospaceRecord<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait MorphospaceRecordResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: MorphospaceRecordHandle<H>) -> Option<MorphospaceRecordRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `MorphospaceRecord<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct MorphospaceRecordRecord<H: HostTypes> {
    pub boundary_type: AchievabilityStatus,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `MorphospaceRecord<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedMorphospaceRecord<'r, R: MorphospaceRecordResolver<H>, H: HostTypes> {
    handle: MorphospaceRecordHandle<H>,
    resolver: &'r R,
    record: Option<MorphospaceRecordRecord<H>>,
}
impl<'r, R: MorphospaceRecordResolver<H>, H: HostTypes> ResolvedMorphospaceRecord<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: MorphospaceRecordHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> MorphospaceRecordHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&MorphospaceRecordRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: MorphospaceRecordResolver<H>, H: HostTypes> MorphospaceRecord<H>
    for ResolvedMorphospaceRecord<'r, R, H>
{
    fn boundary_type(&self) -> AchievabilityStatus {
        match &self.record {
            Some(r) => r.boundary_type,
            None => <AchievabilityStatus>::default(),
        }
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `MorphospaceBoundary<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct MorphospaceBoundaryHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for MorphospaceBoundaryHandle<H> {}
impl<H: HostTypes> Clone for MorphospaceBoundaryHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for MorphospaceBoundaryHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for MorphospaceBoundaryHandle<H> {}
impl<H: HostTypes> core::hash::Hash for MorphospaceBoundaryHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> MorphospaceBoundaryHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `MorphospaceBoundary<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait MorphospaceBoundaryResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: MorphospaceBoundaryHandle<H>)
        -> Option<MorphospaceBoundaryRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `MorphospaceBoundary<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct MorphospaceBoundaryRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `MorphospaceBoundary<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedMorphospaceBoundary<'r, R: MorphospaceBoundaryResolver<H>, H: HostTypes> {
    handle: MorphospaceBoundaryHandle<H>,
    resolver: &'r R,
    record: Option<MorphospaceBoundaryRecord<H>>,
}
impl<'r, R: MorphospaceBoundaryResolver<H>, H: HostTypes> ResolvedMorphospaceBoundary<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: MorphospaceBoundaryHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> MorphospaceBoundaryHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&MorphospaceBoundaryRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: MorphospaceBoundaryResolver<H>, H: HostTypes> MorphospaceBoundary<H>
    for ResolvedMorphospaceBoundary<'r, R, H>
{
    type MorphospaceRecord = NullMorphospaceRecord<H>;
    fn morphospace_record(&self) -> &[Self::MorphospaceRecord] {
        &[]
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `InductiveProof<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct InductiveProofHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for InductiveProofHandle<H> {}
impl<H: HostTypes> Clone for InductiveProofHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for InductiveProofHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for InductiveProofHandle<H> {}
impl<H: HostTypes> core::hash::Hash for InductiveProofHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> InductiveProofHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `InductiveProof<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait InductiveProofResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: InductiveProofHandle<H>) -> Option<InductiveProofRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `InductiveProof<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct InductiveProofRecord<H: HostTypes> {
    pub base_case_handle: ProofHandle<H>,
    pub inductive_step_handle: ProofHandle<H>,
    pub valid_for_kat_least: u64,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `InductiveProof<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedInductiveProof<'r, R: InductiveProofResolver<H>, H: HostTypes> {
    handle: InductiveProofHandle<H>,
    resolver: &'r R,
    record: Option<InductiveProofRecord<H>>,
}
impl<'r, R: InductiveProofResolver<H>, H: HostTypes> ResolvedInductiveProof<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: InductiveProofHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> InductiveProofHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&InductiveProofRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: InductiveProofResolver<H>, H: HostTypes> Proof<H> for ResolvedInductiveProof<'r, R, H> {
    fn verified(&self) -> bool {
        false
    }
    fn timestamp(&self) -> &H::WitnessBytes {
        H::EMPTY_WITNESS_BYTES
    }
    type WitnessData = NullWitnessData<H>;
    fn witness(&self) -> &[Self::WitnessData] {
        &[]
    }
    type Identity = crate::kernel::op::NullIdentity<H>;
    fn proves_identity(&self) -> &Self::Identity {
        &<crate::kernel::op::NullIdentity<H>>::ABSENT
    }
    fn verified_at_level(&self) -> &[WittLevel] {
        &[]
    }
    fn strategy(&self) -> ProofStrategy {
        <ProofStrategy>::default()
    }
    fn depends_on(&self) -> &[Self::Identity] {
        &[]
    }
    type DerivationTerm = NullDerivationTerm<H>;
    fn formal_derivation(&self) -> &Self::DerivationTerm {
        &<NullDerivationTerm<H>>::ABSENT
    }
}
impl<'r, R: InductiveProofResolver<H>, H: HostTypes> InductiveProof<H>
    for ResolvedInductiveProof<'r, R, H>
{
    type Proof = NullProof<H>;
    fn base_case(&self) -> &Self::Proof {
        &<NullProof<H>>::ABSENT
    }
    fn inductive_step(&self) -> &Self::Proof {
        &<NullProof<H>>::ABSENT
    }
    fn valid_for_kat_least(&self) -> u64 {
        match &self.record {
            Some(r) => r.valid_for_kat_least,
            None => 0,
        }
    }
}
impl<'r, R: InductiveProofResolver<H>, H: HostTypes> ResolvedInductiveProof<'r, R, H> {
    /// Promote the `base_case` handle on the cached record into a
    /// resolved wrapper, given a resolver for the range class.
    /// Returns `None` if no record was resolved at construction.
    #[inline]
    pub fn resolve_base_case<'r2, R2: ProofResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedProof<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedProof::new(record.base_case_handle, r))
    }
    /// Promote the `inductive_step` handle on the cached record into a
    /// resolved wrapper, given a resolver for the range class.
    /// Returns `None` if no record was resolved at construction.
    #[inline]
    pub fn resolve_inductive_step<'r2, R2: ProofResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedProof<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedProof::new(record.inductive_step_handle, r))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `DerivationTerm<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct DerivationTermHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for DerivationTermHandle<H> {}
impl<H: HostTypes> Clone for DerivationTermHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for DerivationTermHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for DerivationTermHandle<H> {}
impl<H: HostTypes> core::hash::Hash for DerivationTermHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> DerivationTermHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `DerivationTerm<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait DerivationTermResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: DerivationTermHandle<H>) -> Option<DerivationTermRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `DerivationTerm<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct DerivationTermRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `DerivationTerm<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedDerivationTerm<'r, R: DerivationTermResolver<H>, H: HostTypes> {
    handle: DerivationTermHandle<H>,
    resolver: &'r R,
    record: Option<DerivationTermRecord<H>>,
}
impl<'r, R: DerivationTermResolver<H>, H: HostTypes> ResolvedDerivationTerm<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: DerivationTermHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> DerivationTermHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&DerivationTermRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: DerivationTermResolver<H>, H: HostTypes> DerivationTerm<H>
    for ResolvedDerivationTerm<'r, R, H>
{
}

/// Phase 8 (orphan-closure) — content-addressed handle for `TacticApplication<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct TacticApplicationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for TacticApplicationHandle<H> {}
impl<H: HostTypes> Clone for TacticApplicationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for TacticApplicationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for TacticApplicationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for TacticApplicationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> TacticApplicationHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `TacticApplication<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait TacticApplicationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: TacticApplicationHandle<H>) -> Option<TacticApplicationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `TacticApplication<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct TacticApplicationRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `TacticApplication<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedTacticApplication<'r, R: TacticApplicationResolver<H>, H: HostTypes> {
    handle: TacticApplicationHandle<H>,
    resolver: &'r R,
    record: Option<TacticApplicationRecord<H>>,
}
impl<'r, R: TacticApplicationResolver<H>, H: HostTypes> ResolvedTacticApplication<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: TacticApplicationHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> TacticApplicationHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&TacticApplicationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: TacticApplicationResolver<H>, H: HostTypes> DerivationTerm<H>
    for ResolvedTacticApplication<'r, R, H>
{
}
impl<'r, R: TacticApplicationResolver<H>, H: HostTypes> TacticApplication<H>
    for ResolvedTacticApplication<'r, R, H>
{
}

/// Phase 8 (orphan-closure) — content-addressed handle for `LemmaInvocation<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct LemmaInvocationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for LemmaInvocationHandle<H> {}
impl<H: HostTypes> Clone for LemmaInvocationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for LemmaInvocationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for LemmaInvocationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for LemmaInvocationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> LemmaInvocationHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `LemmaInvocation<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait LemmaInvocationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: LemmaInvocationHandle<H>) -> Option<LemmaInvocationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `LemmaInvocation<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct LemmaInvocationRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `LemmaInvocation<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedLemmaInvocation<'r, R: LemmaInvocationResolver<H>, H: HostTypes> {
    handle: LemmaInvocationHandle<H>,
    resolver: &'r R,
    record: Option<LemmaInvocationRecord<H>>,
}
impl<'r, R: LemmaInvocationResolver<H>, H: HostTypes> ResolvedLemmaInvocation<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: LemmaInvocationHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> LemmaInvocationHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&LemmaInvocationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: LemmaInvocationResolver<H>, H: HostTypes> DerivationTerm<H>
    for ResolvedLemmaInvocation<'r, R, H>
{
}
impl<'r, R: LemmaInvocationResolver<H>, H: HostTypes> LemmaInvocation<H>
    for ResolvedLemmaInvocation<'r, R, H>
{
}

/// Phase 8 (orphan-closure) — content-addressed handle for `InductionStep<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct InductionStepHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for InductionStepHandle<H> {}
impl<H: HostTypes> Clone for InductionStepHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for InductionStepHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for InductionStepHandle<H> {}
impl<H: HostTypes> core::hash::Hash for InductionStepHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> InductionStepHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `InductionStep<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait InductionStepResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: InductionStepHandle<H>) -> Option<InductionStepRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `InductionStep<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct InductionStepRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `InductionStep<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedInductionStep<'r, R: InductionStepResolver<H>, H: HostTypes> {
    handle: InductionStepHandle<H>,
    resolver: &'r R,
    record: Option<InductionStepRecord<H>>,
}
impl<'r, R: InductionStepResolver<H>, H: HostTypes> ResolvedInductionStep<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: InductionStepHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> InductionStepHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&InductionStepRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: InductionStepResolver<H>, H: HostTypes> DerivationTerm<H>
    for ResolvedInductionStep<'r, R, H>
{
}
impl<'r, R: InductionStepResolver<H>, H: HostTypes> InductionStep<H>
    for ResolvedInductionStep<'r, R, H>
{
}

/// Phase 8 (orphan-closure) — content-addressed handle for `ComputationStep<H>`.
///
/// Pairs a [`crate::enforcement::ContentFingerprint`] with a phantom
/// `H` so type-state checks can't mix handles across `HostTypes` impls.
#[derive(Debug)]
pub struct ComputationStepHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for ComputationStepHandle<H> {}
impl<H: HostTypes> Clone for ComputationStepHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for ComputationStepHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for ComputationStepHandle<H> {}
impl<H: HostTypes> core::hash::Hash for ComputationStepHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> ComputationStepHandle<H> {
    /// Construct a handle from its content fingerprint.
    #[inline]
    #[must_use]
    pub const fn new(fingerprint: crate::enforcement::ContentFingerprint) -> Self {
        Self {
            fingerprint,
            _phantom: core::marker::PhantomData,
        }
    }
}

/// Phase 8 (orphan-closure) — resolver trait for `ComputationStep<H>`.
///
/// Hosts implement this trait to map a handle into a typed record.
/// The default Null stub does not implement this trait — it carries
/// no record. Resolution is the responsibility of the host pipeline.
pub trait ComputationStepResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: ComputationStepHandle<H>) -> Option<ComputationStepRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `ComputationStep<H>`.
///
/// Carries a field per functional accessor of the trait. Object
/// fields hold `{Range}Handle<H>`; iterate via the Resolved wrapper
/// chain-resolver methods.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct ComputationStepRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `ComputationStep<H>`.
///
/// Caches the resolver's lookup at construction. Accessors return
/// the cached record's fields when present, falling back to the
/// `Null{Class}<H>` absent sentinels when the resolver returned
/// `None`. Object accessors always return absent sentinels — use
/// the `resolve_{m}` chain methods to descend into sub-records.
pub struct ResolvedComputationStep<'r, R: ComputationStepResolver<H>, H: HostTypes> {
    handle: ComputationStepHandle<H>,
    resolver: &'r R,
    record: Option<ComputationStepRecord<H>>,
}
impl<'r, R: ComputationStepResolver<H>, H: HostTypes> ResolvedComputationStep<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: ComputationStepHandle<H>, resolver: &'r R) -> Self {
        let record = resolver.resolve(handle);
        Self {
            handle,
            resolver,
            record,
        }
    }
    /// The handle this wrapper resolves.
    #[inline]
    #[must_use]
    pub const fn handle(&self) -> ComputationStepHandle<H> {
        self.handle
    }
    /// The resolver supplied at construction.
    #[inline]
    #[must_use]
    pub const fn resolver(&self) -> &'r R {
        self.resolver
    }
    /// The cached record, or `None` when the resolver returned `None`.
    #[inline]
    #[must_use]
    pub const fn record(&self) -> Option<&ComputationStepRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: ComputationStepResolver<H>, H: HostTypes> DerivationTerm<H>
    for ResolvedComputationStep<'r, R, H>
{
}
impl<'r, R: ComputationStepResolver<H>, H: HostTypes> ComputationStep<H>
    for ResolvedComputationStep<'r, R, H>
{
}

/// Follows from ZMod ring axioms. Lean4 tactic: `by ring`.
pub mod ring_axiom {}

/// Decidable at Q0 by exhaustive evaluation. Lean4: `by native_decide`.
pub mod decide_q0 {}

/// Induction on bit width n. Lean4: `by induction n`.
pub mod bitwise_induction {}

/// From dihedral group presentation. Lean4: `by group`.
pub mod group_presentation {}

/// By simplification with cited lemmas. Lean4: `by simp \[lemmalist\]`.
pub mod simplification {}

/// By Chinese Remainder Theorem. Lean4: `by exact ZMod.chineseRemainder ...`.
pub mod chinese_remainder {}

/// By Euler-Poincare formula applied to the constraint nerve.
pub mod euler_poincare {}

/// By Ostrowski product formula or derived valuation arguments.
pub mod product_formula {}

/// By composing proofs of sub-identities. Lean4: `by exact ...`.
pub mod composition {}

/// By deriving contradiction for impossibility witnesses. Lean4: `by contradiction`.
pub mod contradiction {}

/// By computation at a specified quantum level. Lean4: `by native_decide`.
pub mod computation {}

/// Computation certificate for the critical identity neg(bnot(x)) = succ(x) at Q0.
pub mod prf_critical_identity {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `criticalIdentity`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/criticalIdentity";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of the critical identity neg(bnot(x)) = succ(x). Holds at all quantum levels.
pub mod prf_critical_identity_axiomatic {
    /// `provesIdentity` -> `criticalIdentity`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/criticalIdentity";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for phi_1 at Q0.
pub mod prf_phi_1 {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `phi_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/phi_1";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for phi_2 at Q0.
pub mod prf_phi_2 {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `phi_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/phi_2";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for phi_3 at Q0.
pub mod prf_phi_3 {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `phi_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/phi_3";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for phi_4 at Q0.
pub mod prf_phi_4 {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `phi_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/phi_4";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for phi_5 at Q0.
pub mod prf_phi_5 {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `phi_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/phi_5";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for phi_6 at Q0.
pub mod prf_phi_6 {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `phi_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/phi_6";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AD_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ad_1 {
    /// `provesIdentity` -> `AD_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AD_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AD_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ad_2 {
    /// `provesIdentity` -> `AD_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AD_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_A1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_a1 {
    /// `provesIdentity` -> `R_A1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_A1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_A2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_a2 {
    /// `provesIdentity` -> `R_A2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_A2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_A3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_a3 {
    /// `provesIdentity` -> `R_A3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_A3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_A4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_a4 {
    /// `provesIdentity` -> `R_A4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_A4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_A5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_a5 {
    /// `provesIdentity` -> `R_A5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_A5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_A6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_a6 {
    /// `provesIdentity` -> `R_A6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_A6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_M1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_m1 {
    /// `provesIdentity` -> `R_M1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_M1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_M2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_m2 {
    /// `provesIdentity` -> `R_M2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_M2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_M3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_m3 {
    /// `provesIdentity` -> `R_M3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_M3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_M4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_m4 {
    /// `provesIdentity` -> `R_M4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_M4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of R_M5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_r_m5 {
    /// `provesIdentity` -> `R_M5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/R_M5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_1 {
    /// `provesIdentity` -> `B_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_1";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_2 {
    /// `provesIdentity` -> `B_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_2";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_3 {
    /// `provesIdentity` -> `B_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_3";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_4 {
    /// `provesIdentity` -> `B_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_4";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_5 {
    /// `provesIdentity` -> `B_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_5";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_6 {
    /// `provesIdentity` -> `B_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_6";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_7. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_7 {
    /// `provesIdentity` -> `B_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_7";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_8. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_8 {
    /// `provesIdentity` -> `B_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_8";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_9. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_9 {
    /// `provesIdentity` -> `B_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_9";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_10. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_10 {
    /// `provesIdentity` -> `B_10`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_10";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_11. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_11 {
    /// `provesIdentity` -> `B_11`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_11";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_12. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_12 {
    /// `provesIdentity` -> `B_12`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_12";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of B_13. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_b_13 {
    /// `provesIdentity` -> `B_13`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/B_13";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of X_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_x_1 {
    /// `provesIdentity` -> `X_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/X_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of X_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_x_2 {
    /// `provesIdentity` -> `X_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/X_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of X_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_x_3 {
    /// `provesIdentity` -> `X_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/X_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of X_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_x_4 {
    /// `provesIdentity` -> `X_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/X_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of X_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_x_5 {
    /// `provesIdentity` -> `X_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/X_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of X_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_x_6 {
    /// `provesIdentity` -> `X_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/X_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of X_7. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_x_7 {
    /// `provesIdentity` -> `X_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/X_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of D_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_d_1 {
    /// `provesIdentity` -> `D_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/D_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of D_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_d_3 {
    /// `provesIdentity` -> `D_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/D_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of D_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_d_4 {
    /// `provesIdentity` -> `D_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/D_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of D_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_d_5 {
    /// `provesIdentity` -> `D_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/D_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of U_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_u_1 {
    /// `provesIdentity` -> `U_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/U_1";
    /// `strategy` -> `ChineseRemainder`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ChineseRemainder";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of U_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_u_2 {
    /// `provesIdentity` -> `U_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/U_2";
    /// `strategy` -> `ChineseRemainder`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ChineseRemainder";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of U_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_u_3 {
    /// `provesIdentity` -> `U_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/U_3";
    /// `strategy` -> `ChineseRemainder`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ChineseRemainder";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of U_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_u_4 {
    /// `provesIdentity` -> `U_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/U_4";
    /// `strategy` -> `ChineseRemainder`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ChineseRemainder";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of U_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_u_5 {
    /// `provesIdentity` -> `U_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/U_5";
    /// `strategy` -> `ChineseRemainder`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ChineseRemainder";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AG_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ag_1 {
    /// `provesIdentity` -> `AG_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AG_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AG_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ag_2 {
    /// `provesIdentity` -> `AG_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AG_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AG_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ag_3 {
    /// `provesIdentity` -> `AG_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AG_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AG_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ag_4 {
    /// `provesIdentity` -> `AG_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AG_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CA_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ca_1 {
    /// `provesIdentity` -> `CA_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CA_1";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CA_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ca_2 {
    /// `provesIdentity` -> `CA_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CA_2";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CA_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ca_3 {
    /// `provesIdentity` -> `CA_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CA_3";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CA_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ca_4 {
    /// `provesIdentity` -> `CA_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CA_4";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CA_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ca_5 {
    /// `provesIdentity` -> `CA_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CA_5";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CA_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ca_6 {
    /// `provesIdentity` -> `CA_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CA_6";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of C_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_c_1 {
    /// `provesIdentity` -> `C_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/C_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of C_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_c_2 {
    /// `provesIdentity` -> `C_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/C_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of C_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_c_3 {
    /// `provesIdentity` -> `C_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/C_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of C_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_c_4 {
    /// `provesIdentity` -> `C_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/C_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of C_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_c_5 {
    /// `provesIdentity` -> `C_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/C_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of C_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_c_6 {
    /// `provesIdentity` -> `C_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/C_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CDI. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cdi {
    /// `provesIdentity` -> `CDI`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CDI";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CL_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cl_1 {
    /// `provesIdentity` -> `CL_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CL_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CL_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cl_2 {
    /// `provesIdentity` -> `CL_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CL_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CL_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cl_3 {
    /// `provesIdentity` -> `CL_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CL_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CL_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cl_4 {
    /// `provesIdentity` -> `CL_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CL_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CL_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cl_5 {
    /// `provesIdentity` -> `CL_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CL_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CM_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cm_1 {
    /// `provesIdentity` -> `CM_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CM_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CM_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cm_2 {
    /// `provesIdentity` -> `CM_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CM_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CM_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cm_3 {
    /// `provesIdentity` -> `CM_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CM_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CR_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cr_1 {
    /// `provesIdentity` -> `CR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CR_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CR_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cr_2 {
    /// `provesIdentity` -> `CR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CR_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CR_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cr_3 {
    /// `provesIdentity` -> `CR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CR_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CR_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cr_4 {
    /// `provesIdentity` -> `CR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CR_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CR_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cr_5 {
    /// `provesIdentity` -> `CR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CR_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of F_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_f_1 {
    /// `provesIdentity` -> `F_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/F_1";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of F_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_f_2 {
    /// `provesIdentity` -> `F_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/F_2";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of F_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_f_3 {
    /// `provesIdentity` -> `F_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/F_3";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of F_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_f_4 {
    /// `provesIdentity` -> `F_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/F_4";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FL_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fl_1 {
    /// `provesIdentity` -> `FL_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FL_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FL_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fl_2 {
    /// `provesIdentity` -> `FL_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FL_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FL_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fl_3 {
    /// `provesIdentity` -> `FL_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FL_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FL_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fl_4 {
    /// `provesIdentity` -> `FL_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FL_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FPM_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fpm_1 {
    /// `provesIdentity` -> `FPM_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FPM_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fpm_2 {
    /// `provesIdentity` -> `FPM_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FPM_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fpm_3 {
    /// `provesIdentity` -> `FPM_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FPM_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fpm_4 {
    /// `provesIdentity` -> `FPM_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FPM_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fpm_5 {
    /// `provesIdentity` -> `FPM_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FPM_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fpm_6 {
    /// `provesIdentity` -> `FPM_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FPM_7. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fpm_7 {
    /// `provesIdentity` -> `FPM_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FS_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fs_1 {
    /// `provesIdentity` -> `FS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FS_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FS_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fs_2 {
    /// `provesIdentity` -> `FS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FS_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FS_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fs_3 {
    /// `provesIdentity` -> `FS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FS_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FS_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fs_4 {
    /// `provesIdentity` -> `FS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FS_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FS_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fs_5 {
    /// `provesIdentity` -> `FS_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FS_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FS_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fs_6 {
    /// `provesIdentity` -> `FS_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FS_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FS_7. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_fs_7 {
    /// `provesIdentity` -> `FS_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FS_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RE_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_re_1 {
    /// `provesIdentity` -> `RE_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RE_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IR_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ir_1 {
    /// `provesIdentity` -> `IR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IR_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IR_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ir_2 {
    /// `provesIdentity` -> `IR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IR_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IR_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ir_3 {
    /// `provesIdentity` -> `IR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IR_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IR_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ir_4 {
    /// `provesIdentity` -> `IR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IR_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SF_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_sf_1 {
    /// `provesIdentity` -> `SF_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SF_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SF_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_sf_2 {
    /// `provesIdentity` -> `SF_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SF_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RD_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_rd_1 {
    /// `provesIdentity` -> `RD_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RD_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RD_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_rd_2 {
    /// `provesIdentity` -> `RD_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RD_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SE_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_se_1 {
    /// `provesIdentity` -> `SE_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SE_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SE_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_se_2 {
    /// `provesIdentity` -> `SE_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SE_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SE_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_se_3 {
    /// `provesIdentity` -> `SE_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SE_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SE_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_se_4 {
    /// `provesIdentity` -> `SE_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SE_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OO_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_oo_1 {
    /// `provesIdentity` -> `OO_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OO_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OO_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_oo_2 {
    /// `provesIdentity` -> `OO_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OO_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OO_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_oo_3 {
    /// `provesIdentity` -> `OO_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OO_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OO_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_oo_4 {
    /// `provesIdentity` -> `OO_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OO_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OO_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_oo_5 {
    /// `provesIdentity` -> `OO_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OO_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CB_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cb_1 {
    /// `provesIdentity` -> `CB_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CB_1";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CB_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cb_2 {
    /// `provesIdentity` -> `CB_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CB_2";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CB_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cb_3 {
    /// `provesIdentity` -> `CB_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CB_3";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CB_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cb_4 {
    /// `provesIdentity` -> `CB_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CB_4";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CB_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cb_5 {
    /// `provesIdentity` -> `CB_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CB_5";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CB_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cb_6 {
    /// `provesIdentity` -> `CB_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CB_6";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_M1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_m1 {
    /// `provesIdentity` -> `OB_M1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_M1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_M2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_m2 {
    /// `provesIdentity` -> `OB_M2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_M2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_M3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_m3 {
    /// `provesIdentity` -> `OB_M3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_M3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_M4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_m4 {
    /// `provesIdentity` -> `OB_M4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_M4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_M5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_m5 {
    /// `provesIdentity` -> `OB_M5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_M5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_M6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_m6 {
    /// `provesIdentity` -> `OB_M6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_M6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_C1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_c1 {
    /// `provesIdentity` -> `OB_C1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_C1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_C2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_c2 {
    /// `provesIdentity` -> `OB_C2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_C2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_C3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_c3 {
    /// `provesIdentity` -> `OB_C3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_C3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_H1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_h1 {
    /// `provesIdentity` -> `OB_H1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_H1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_H2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_h2 {
    /// `provesIdentity` -> `OB_H2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_H2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_H3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_h3 {
    /// `provesIdentity` -> `OB_H3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_H3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_P1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_p1 {
    /// `provesIdentity` -> `OB_P1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_P1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_P2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_p2 {
    /// `provesIdentity` -> `OB_P2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_P2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OB_P3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ob_p3 {
    /// `provesIdentity` -> `OB_P3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OB_P3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CT_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ct_1 {
    /// `provesIdentity` -> `CT_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CT_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CT_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ct_2 {
    /// `provesIdentity` -> `CT_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CT_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CT_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ct_3 {
    /// `provesIdentity` -> `CT_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CT_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CT_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ct_4 {
    /// `provesIdentity` -> `CT_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CT_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CF_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cf_1 {
    /// `provesIdentity` -> `CF_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CF_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CF_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cf_2 {
    /// `provesIdentity` -> `CF_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CF_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CF_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cf_3 {
    /// `provesIdentity` -> `CF_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CF_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CF_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_cf_4 {
    /// `provesIdentity` -> `CF_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CF_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HG_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_hg_1 {
    /// `provesIdentity` -> `HG_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HG_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HG_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_hg_2 {
    /// `provesIdentity` -> `HG_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HG_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HG_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_hg_3 {
    /// `provesIdentity` -> `HG_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HG_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HG_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_hg_4 {
    /// `provesIdentity` -> `HG_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HG_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HG_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_hg_5 {
    /// `provesIdentity` -> `HG_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HG_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_C1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_c1 {
    /// `provesIdentity` -> `T_C1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_C1";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_C2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_c2 {
    /// `provesIdentity` -> `T_C2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_C2";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_C3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_c3 {
    /// `provesIdentity` -> `T_C3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_C3";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_C4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_c4 {
    /// `provesIdentity` -> `T_C4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_C4";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_I1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_i1 {
    /// `provesIdentity` -> `T_I1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_I1";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_I2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_i2 {
    /// `provesIdentity` -> `T_I2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_I2";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_I3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_i3 {
    /// `provesIdentity` -> `T_I3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_I3";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_I4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_i4 {
    /// `provesIdentity` -> `T_I4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_I4";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_I5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_i5 {
    /// `provesIdentity` -> `T_I5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_I5";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_E1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_e1 {
    /// `provesIdentity` -> `T_E1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_E1";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_E2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_e2 {
    /// `provesIdentity` -> `T_E2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_E2";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_E3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_e3 {
    /// `provesIdentity` -> `T_E3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_E3";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_E4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_e4 {
    /// `provesIdentity` -> `T_E4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_E4";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_A1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_a1 {
    /// `provesIdentity` -> `T_A1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_A1";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_A2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_a2 {
    /// `provesIdentity` -> `T_A2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_A2";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_A3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_a3 {
    /// `provesIdentity` -> `T_A3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_A3";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of T_A4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_t_a4 {
    /// `provesIdentity` -> `T_A4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/T_A4";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AU_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_au_1 {
    /// `provesIdentity` -> `AU_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AU_1";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AU_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_au_2 {
    /// `provesIdentity` -> `AU_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AU_2";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AU_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_au_3 {
    /// `provesIdentity` -> `AU_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AU_3";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AU_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_au_4 {
    /// `provesIdentity` -> `AU_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AU_4";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AU_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_au_5 {
    /// `provesIdentity` -> `AU_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AU_5";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EF_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ef_1 {
    /// `provesIdentity` -> `EF_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EF_1";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EF_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ef_2 {
    /// `provesIdentity` -> `EF_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EF_2";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EF_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ef_3 {
    /// `provesIdentity` -> `EF_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EF_3";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EF_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ef_4 {
    /// `provesIdentity` -> `EF_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EF_4";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EF_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ef_5 {
    /// `provesIdentity` -> `EF_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EF_5";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EF_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ef_6 {
    /// `provesIdentity` -> `EF_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EF_6";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EF_7. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ef_7 {
    /// `provesIdentity` -> `EF_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EF_7";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AA_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_aa_1 {
    /// `provesIdentity` -> `AA_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AA_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AA_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_aa_2 {
    /// `provesIdentity` -> `AA_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AA_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AA_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_aa_3 {
    /// `provesIdentity` -> `AA_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AA_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AA_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_aa_4 {
    /// `provesIdentity` -> `AA_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AA_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AA_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_aa_5 {
    /// `provesIdentity` -> `AA_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AA_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AA_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_aa_6 {
    /// `provesIdentity` -> `AA_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AA_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AM_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_am_1 {
    /// `provesIdentity` -> `AM_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AM_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AM_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_am_2 {
    /// `provesIdentity` -> `AM_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AM_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AM_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_am_3 {
    /// `provesIdentity` -> `AM_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AM_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AM_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_am_4 {
    /// `provesIdentity` -> `AM_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AM_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_1 {
    /// `provesIdentity` -> `TH_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_2 {
    /// `provesIdentity` -> `TH_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_3 {
    /// `provesIdentity` -> `TH_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_4 {
    /// `provesIdentity` -> `TH_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_5 {
    /// `provesIdentity` -> `TH_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_6 {
    /// `provesIdentity` -> `TH_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_7. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_7 {
    /// `provesIdentity` -> `TH_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_8. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_8 {
    /// `provesIdentity` -> `TH_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_8";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_9. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_9 {
    /// `provesIdentity` -> `TH_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_9";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TH_10. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_th_10 {
    /// `provesIdentity` -> `TH_10`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TH_10";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AR_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ar_1 {
    /// `provesIdentity` -> `AR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AR_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AR_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ar_2 {
    /// `provesIdentity` -> `AR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AR_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AR_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ar_3 {
    /// `provesIdentity` -> `AR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AR_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AR_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ar_4 {
    /// `provesIdentity` -> `AR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AR_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive proof of AR_5: greedy vs adiabatic cost difference is at most 5%. Base case at Q0 by exhaustive evaluation; inductive step by QLS_5 (identity preservation under lift).
pub mod prf_ar_5 {
    /// `baseCase` -> `prf_AR_5_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_AR_5_base";
    /// `inductiveStep` -> `prf_AR_5_step`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_AR_5_step";
    /// `provesIdentity` -> `AR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AR_5";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PD_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_pd_1 {
    /// `provesIdentity` -> `PD_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PD_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PD_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_pd_2 {
    /// `provesIdentity` -> `PD_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PD_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PD_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_pd_3 {
    /// `provesIdentity` -> `PD_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PD_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PD_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_pd_4 {
    /// `provesIdentity` -> `PD_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PD_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PD_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_pd_5 {
    /// `provesIdentity` -> `PD_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PD_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RC_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_rc_1 {
    /// `provesIdentity` -> `RC_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RC_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RC_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_rc_2 {
    /// `provesIdentity` -> `RC_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RC_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RC_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_rc_3 {
    /// `provesIdentity` -> `RC_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RC_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RC_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_rc_4 {
    /// `provesIdentity` -> `RC_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RC_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RC_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_rc_5 {
    /// `provesIdentity` -> `RC_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RC_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_1 {
    /// `provesIdentity` -> `DC_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_2 {
    /// `provesIdentity` -> `DC_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_3 {
    /// `provesIdentity` -> `DC_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_4. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_4 {
    /// `provesIdentity` -> `DC_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_5 {
    /// `provesIdentity` -> `DC_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_6 {
    /// `provesIdentity` -> `DC_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_7. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_7 {
    /// `provesIdentity` -> `DC_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_8. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_8 {
    /// `provesIdentity` -> `DC_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_8";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_9. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_9 {
    /// `provesIdentity` -> `DC_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_9";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_10. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_10 {
    /// `provesIdentity` -> `DC_10`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_10";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DC_11. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_dc_11 {
    /// `provesIdentity` -> `DC_11`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DC_11";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HA_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ha_1 {
    /// `provesIdentity` -> `HA_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HA_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HA_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ha_2 {
    /// `provesIdentity` -> `HA_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HA_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HA_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_ha_3 {
    /// `provesIdentity` -> `HA_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HA_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IT_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_it_2 {
    /// `provesIdentity` -> `IT_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IT_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IT_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_it_3 {
    /// `provesIdentity` -> `IT_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IT_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IT_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_it_6 {
    /// `provesIdentity` -> `IT_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IT_6";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IT_7a. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_it_7a {
    /// `provesIdentity` -> `IT_7a`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IT_7a";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IT_7b. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_it_7b {
    /// `provesIdentity` -> `IT_7b`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IT_7b";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IT_7c. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_it_7c {
    /// `provesIdentity` -> `IT_7c`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IT_7c";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IT_7d. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_it_7d {
    /// `provesIdentity` -> `IT_7d`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IT_7d";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of psi_1. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_psi_1 {
    /// `provesIdentity` -> `psi_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/psi_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of psi_2. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_psi_2 {
    /// `provesIdentity` -> `psi_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/psi_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of psi_3. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_psi_3 {
    /// `provesIdentity` -> `psi_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/psi_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of psi_5. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_psi_5 {
    /// `provesIdentity` -> `psi_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/psi_5";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of psi_6. Holds at all quantum levels by definition of Z/(2^n)Z.
pub mod prf_psi_6 {
    /// `provesIdentity` -> `psi_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/psi_6";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of homology:boundarySquaredZero. Holds at all quantum levels by topological reasoning.
pub mod prf_boundary_squared_zero {
    /// `provesIdentity` -> `boundarySquaredZero`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/homology/boundarySquaredZero";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of homology:psi_4. Holds at all quantum levels by topological reasoning.
pub mod prf_psi_4 {
    /// `provesIdentity` -> `psi_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/homology/psi_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of homology:indexBridge. Holds at all quantum levels by topological reasoning.
pub mod prf_index_bridge {
    /// `provesIdentity` -> `indexBridge`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/homology/indexBridge";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of cohomology:coboundarySquaredZero. Holds at all quantum levels by topological reasoning.
pub mod prf_coboundary_squared_zero {
    /// `provesIdentity` -> `coboundarySquaredZero`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/cohomology/coboundarySquaredZero";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of cohomology:deRhamDuality. Holds at all quantum levels by topological reasoning.
pub mod prf_de_rham_duality {
    /// `provesIdentity` -> `deRhamDuality`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/cohomology/deRhamDuality";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of cohomology:sheafCohomologyBridge. Holds at all quantum levels by topological reasoning.
pub mod prf_sheaf_cohomology_bridge {
    /// `provesIdentity` -> `sheafCohomologyBridge`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/cohomology/sheafCohomologyBridge";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of cohomology:localGlobalPrinciple. Holds at all quantum levels by topological reasoning.
pub mod prf_local_global_principle {
    /// `provesIdentity` -> `localGlobalPrinciple`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/cohomology/localGlobalPrinciple";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of the Surface Symmetry Theorem. Holds at all quantum levels: the composite P∘Π∘G is a well-typed morphism whenever G and P share the same state:Frame. Follows from the definition of the shared-frame condition and the type-equivalence algebra.
pub mod prf_surface_symmetry {
    /// `provesIdentity` -> `surfaceSymmetry`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/surfaceSymmetry";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof that a CompleteType T satisfies: resolution(x, T) terminates in O(1) for all x ∈ R_n. Follows from IT_7d: when χ(N(C)) = n and all β_k = 0, the resolver has no topological obstructions.
pub mod prf_cc_1 {
    /// `provesIdentity` -> `CC_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CC_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof that the ψ pipeline is monotone: each constraint application cannot increase the site deficit. Derived from the definition of the partition refinement order.
pub mod prf_cc_2 {
    /// `provesIdentity` -> `CC_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CC_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof that a CompletenessCertificate implies CompleteType: the certificate attestation is only issued when IT_7d holds, by construction of the CompletenessResolver.
pub mod prf_cc_3 {
    /// `provesIdentity` -> `CC_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CC_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof that the CompletenessAuditTrail witnessCount equals the number of CompletenessWitness records in the trail. Structural invariant of the audit accumulation protocol.
pub mod prf_cc_4 {
    /// `provesIdentity` -> `CC_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CC_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof that the CechNerve nerve computation is deterministic: the same constraint set always produces the same nerve topology. Follows from the nerve functor being a functor (functoriality).
pub mod prf_cc_5 {
    /// `provesIdentity` -> `CC_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CC_5";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Universal proof that neg(bnot(x)) = succ(x) in Z/(2^n)Z for all n ≥ 1. Derived symbolically from ring axioms: bnot is bitwise complement, neg is two's complement negation, succ is modular increment. The critical identity in universal form.
pub mod prf_ql_1 {
    /// `provesIdentity` -> `QL_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QL_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Universal proof that the ring carrier set size is exactly 2^n for all n ≥ 1. Follows from the definition of Z/(2^n)Z.
pub mod prf_ql_2 {
    /// `provesIdentity` -> `QL_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QL_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Universal proof that Landauer erasure cost scales as n × k_B T ln 2 at quantum level n. Follows from the thermodynamic interpretation: each bit erased from an n-bit ring costs k_B T ln 2.
pub mod prf_ql_3 {
    /// `provesIdentity` -> `QL_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QL_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Universal proof that the dihedral group D_{2^n} action on Z/(2^n)Z is faithful for all n ≥ 1. The stabilizer of any element is trivial under the full dihedral action.
pub mod prf_ql_4 {
    /// `provesIdentity` -> `QL_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QL_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Universal proof that canonical form rewriting terminates at all quantum levels. The rewriting system is terminating by lexicographic descent on the term complexity measure.
pub mod prf_ql_5 {
    /// `provesIdentity` -> `QL_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QL_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Universal proof that the completeness criterion χ(N(C)) = n generalizes to all quantum levels. Derived from the definition of the nerve construction and the Euler characteristic formula for simplicial complexes.
pub mod prf_ql_6 {
    /// `provesIdentity` -> `QL_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QL_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Universal proof of the ring topology Euler characteristic identity: χ = 1 − n at quantum level n. Derived from the CW decomposition of the n-dimensional torus formed by the ring's cyclic group action.
pub mod prf_ql_7 {
    /// `provesIdentity` -> `QL_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QL_7";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of binding monotonicity: freeRank(B_{i+1}) ≤ freeRank(B_i) for all i in a Session. Follows from the definition of the BindingAccumulator: each appended binding either pins sites or is a no-op; it never frees them.
pub mod prf_gr_1 {
    /// `provesIdentity` -> `GR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof that the empty session is the identity element of the session algebra: freeRank(B_0) = total site space. The empty accumulator has no pinned sites by definition.
pub mod prf_gr_2 {
    /// `provesIdentity` -> `GR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of session convergence: a session terminates iff freeRank reaches its minimum (the maximum pinned by the given constraint set). Follows from the compactness of the site space and monotonicity.
pub mod prf_gr_3 {
    /// `provesIdentity` -> `GR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof that disjoint bindings compose without site conflict: if two bindings address disjoint site sets, their composition is well-defined and their union is also a valid binding.
pub mod prf_gr_4 {
    /// `provesIdentity` -> `GR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of contradiction detection correctness: ContradictionBoundary fires iff there exist bindings b, b' in the same Context with the same address, different datum, and same constraint. This is the minimal condition for type contradiction.
pub mod prf_gr_5 {
    /// `provesIdentity` -> `GR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of nerve realisability: for any target profile with χ* ≤ n and β₀* = 1, there exists a ConstrainedType whose constraint nerve realises the target. Follows from the constructive synthesis algorithm.
pub mod prf_ts_1 {
    /// `provesIdentity` -> `TS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of minimal basis bound: the MinimalConstraintBasis for the IT_7d target has size exactly n. Follows from the site-by-site construction and the minimality criterion.
pub mod prf_ts_2 {
    /// `provesIdentity` -> `TS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of synthesis monotonicity: adding a constraint never decreases the Euler characteristic of the constraint nerve. Follows from the nerve inclusion principle.
pub mod prf_ts_3 {
    /// `provesIdentity` -> `TS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of synthesis convergence: the TypeSynthesisResolver terminates in at most n steps. Follows from monotonicity (TS_3) and the finite site budget bound.
pub mod prf_ts_4 {
    /// `provesIdentity` -> `TS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of synthesis-certification duality: a SynthesizedType achieves IT_7d iff the CompletenessResolver certifies it as CompleteType. The duality follows from the shared topological criterion.
pub mod prf_ts_5 {
    /// `provesIdentity` -> `TS_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of Jacobian-guided synthesis efficiency: the Jacobian oracle reduces expected steps from O(n²) to O(n log n). Follows from the information content of the Jacobian at each synthesis step.
pub mod prf_ts_6 {
    /// `provesIdentity` -> `TS_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of unreachable signatures: β₀ = 0 is unreachable by any non-empty ConstrainedType. Follows from the nerve connectedness of non-empty constraint sets.
pub mod prf_ts_7 {
    /// `provesIdentity` -> `TS_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of lift unobstructedness criterion: WittLift T' is CompleteType iff the spectral sequence collapses at E_2. Follows from the Leray spectral sequence of the quantum level extension.
pub mod prf_wls_1 {
    /// `baseCase` -> `prf_WLS_1_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WLS_1_base";
    /// `inductiveStep` -> `prf_WLS_6`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WLS_6";
    /// `provesIdentity` -> `WLS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_1";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of obstruction localisation: a non-trivial LiftObstruction is localised to a specific site at bit position n+1. Follows from the local-to-global structure of the constraint nerve.
pub mod prf_wls_2 {
    /// `baseCase` -> `prf_WLS_2_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WLS_2_base";
    /// `inductiveStep` -> `prf_WLS_2_step`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WLS_2_step";
    /// `provesIdentity` -> `WLS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_2";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of monotone lifting: basisSize(T') = basisSize(T) + 1 for trivially obstructed lifts. Follows from the minimal basis construction at Q_{n+1}.
pub mod prf_wls_3 {
    /// `baseCase` -> `prf_WLS_3_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WLS_3_base";
    /// `inductiveStep` -> `prf_WLS_3_step`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WLS_3_step";
    /// `provesIdentity` -> `WLS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_3";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of spectral sequence convergence bound: the spectral sequence converges by page E_{d+2} for depth-d configurations. Follows from the filtration length of the constraint nerve chain complex.
pub mod prf_wls_4 {
    /// `baseCase` -> `prf_WLS_4_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WLS_4_base";
    /// `inductiveStep` -> `prf_WLS_4_step`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WLS_4_step";
    /// `provesIdentity` -> `WLS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_4";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of universal identity preservation under quantum lifts: every universallyValid identity holds in the lifted ring. Follows from the universal validity definition and ring extension properties.
pub mod prf_wls_5 {
    /// `baseCase` -> `prf_WLS_5_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WLS_5_base";
    /// `inductiveStep` -> `prf_WLS_6`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WLS_6";
    /// `provesIdentity` -> `WLS_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_5";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ψ-pipeline universality for quantum lifts: the ψ-pipeline produces a valid ChainComplex for any WittLift. Follows from the functorial construction of the chain complex.
pub mod prf_wls_6 {
    /// `baseCase` -> `prf_WLS_6_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WLS_6_base";
    /// `inductiveStep` -> `prf_WLS_6_step`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WLS_6_step";
    /// `provesIdentity` -> `WLS_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_6";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QLS_1 at Q0: lift unobstructedness holds trivially for 8-bit rings where the constraint nerve is contractible.
pub mod prf_wls_1_base {
    /// `provesIdentity` -> `WLS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QLS_2 at Q0: obstruction localisation holds at the 8-bit level where sites are directly inspectable.
pub mod prf_wls_2_base {
    /// `provesIdentity` -> `WLS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive step for QLS_2: if obstruction is localised at Q_k, the local-to-global structure of the constraint nerve preserves localisation at Q_{k+1}.
pub mod prf_wls_2_step {
    /// `provesIdentity` -> `WLS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QLS_3 at Q0: monotone lifting basis size increment holds trivially for 8-bit to 16-bit extension.
pub mod prf_wls_3_base {
    /// `provesIdentity` -> `WLS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive step for QLS_3: the minimal basis construction at Q_{k+1} adds exactly one element from the trivially obstructed site.
pub mod prf_wls_3_step {
    /// `provesIdentity` -> `WLS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QLS_4 at Q0: spectral sequence convergence at E_{d+2} holds for 8-bit filtrations by direct computation.
pub mod prf_wls_4_base {
    /// `provesIdentity` -> `WLS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_4";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive step for QLS_4: filtration length at Q_{k+1} extends by at most one page from Q_k, preserving the E_{d+2} bound.
pub mod prf_wls_4_step {
    /// `provesIdentity` -> `WLS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_4";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QLS_5 at Q0: universallyValid identities hold in the 8-bit ring by definition of universal validity.
pub mod prf_wls_5_base {
    /// `provesIdentity` -> `WLS_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_5";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QLS_6 at Q0: the psi-pipeline produces a valid ChainComplex for 8-bit WittLifts by direct construction.
pub mod prf_wls_6_base {
    /// `provesIdentity` -> `WLS_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_6";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive step for QLS_6: the functorial construction of the chain complex commutes with quantum level extension.
pub mod prf_wls_6_step {
    /// `provesIdentity` -> `WLS_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WLS_6";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QT_3: resolved basis size formula holds for chain length 1 by direct construction.
pub mod prf_wt_3_base {
    /// `provesIdentity` -> `WT_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QT_5: LiftChainCertificate existence for tower height 1 follows from single-step certificate issuance.
pub mod prf_wt_5_base {
    /// `provesIdentity` -> `WT_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_5";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for AR_5 at Q0: greedy vs adiabatic cost difference verified by exhaustive enumeration over Z/256Z.
pub mod prf_ar_5_base {
    /// `provesIdentity` -> `AR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AR_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive step for AR_5: if greedy vs adiabatic bound holds at Q_k, it holds at Q_{k+1} by QLS_5 (universal identity preservation under quantum lift).
pub mod prf_ar_5_step {
    /// `provesIdentity` -> `AR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AR_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Base case for QM_6 at Q0: amplitude index set equals monotone pinning trajectories by exhaustive trajectory enumeration over the 8-bit site lattice.
pub mod prf_qm_6_base {
    /// `provesIdentity` -> `QM_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QM_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive step for QM_6: monotone pinning trajectories at Q_{k+1} extend those at Q_k by the site lattice ordering (monotone extension property).
pub mod prf_qm_6_step {
    /// `provesIdentity` -> `QM_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QM_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of holonomy group containment: HolonomyGroup(T) ≤ D_{2^n}. Follows from the fact that all constraint applications are dihedral group elements.
pub mod prf_mn_1 {
    /// `provesIdentity` -> `MN_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MN_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of additive flatness: additive constraints (ResidueConstraint, DepthConstraint) generate only the identity in D_{2^n}. Follows from the additive structure of the dihedral action.
pub mod prf_mn_2 {
    /// `provesIdentity` -> `MN_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MN_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of dihedral generation: neg and bnot together generate D_{2^n}. Follows from the standard presentation of the dihedral group by involutions.
pub mod prf_mn_3 {
    /// `provesIdentity` -> `MN_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MN_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of holonomy-Betti implication: non-trivial holonomy implies β₁ ≥ 1. Follows from the fact that a non-trivial monodromy requires a topological loop in the constraint nerve.
pub mod prf_mn_4 {
    /// `provesIdentity` -> `MN_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MN_4";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CompleteType holonomy: IT_7d (β₁ = 0) implies trivial holonomy (FlatType). Follows from MN_4 contrapositive: trivial holonomy ← β₁ = 0.
pub mod prf_mn_5 {
    /// `provesIdentity` -> `MN_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MN_5";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of monodromy composition: the monodromy map is a group homomorphism from the loop space to D_{2^n}. Follows from the composition of dihedral group elements.
pub mod prf_mn_6 {
    /// `provesIdentity` -> `MN_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MN_6";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of TwistedType obstruction class: a TwistedType always contributes a non-zero class to H²(N(C(T')); ℤ/2ℤ) for any WittLift T'. Follows from MN_4 and the obstruction theory of dihedral torsors.
pub mod prf_mn_7 {
    /// `provesIdentity` -> `MN_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MN_7";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of PT_1: product type site additivity. siteBudget(A × B) = siteBudget(A) + siteBudget(B). Follows from the definition of ProductType as an independent concatenation of site spaces.
pub mod prf_pt_1 {
    /// `provesIdentity` -> `PT_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PT_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of PT_2: product type partition factorisation. partition(A × B) = partition(A) ⊗ partition(B). Follows from the tensor product structure of constraint nerves over independent site spaces.
pub mod prf_pt_2 {
    /// `provesIdentity` -> `PT_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PT_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of PT_3: product type Euler characteristic additivity. χ(N(C(A × B))) = χ(N(C(A))) + χ(N(C(B))). Follows from the Künneth formula applied to the join of constraint nerves.
pub mod prf_pt_3 {
    /// `provesIdentity` -> `PT_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PT_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of PT_4: product type entropy additivity. S(A × B) = S(A) + S(B). Follows from PT_1 (site additivity) and TH_1 (S = freeRank × ln 2).
pub mod prf_pt_4 {
    /// `provesIdentity` -> `PT_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PT_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_1: sum type site budget maximum. siteBudget(A + B) = max(siteBudget(A), siteBudget(B)). Follows from SumType requiring capacity for the larger variant.
pub mod prf_st_1 {
    /// `provesIdentity` -> `ST_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_2: sum type entropy. S(A + B) = ln 2 + max(S(A), S(B)). The ln 2 term accounts for the variant discriminant bit; the max reflects that only one variant is active at a time.
pub mod prf_st_2 {
    /// `provesIdentity` -> `ST_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SC_1: context temperature. T_ctx(C) = freeRank(C) × ln 2 / n. Derived from TH_1 normalized per site.
pub mod prf_gs_1 {
    /// `provesIdentity` -> `GS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GS_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SC_2: saturation degree. σ(C) = (n − freeRank(C)) / n. Definitional identity.
pub mod prf_gs_2 {
    /// `provesIdentity` -> `GS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GS_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SC_3: saturation monotonicity. Corollary of SR_1 through order-reversing SC_2.
pub mod prf_gs_3 {
    /// `provesIdentity` -> `GS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GS_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SC_4: ground state equivalence. Four equivalent conditions for full saturation derived from SC_2, TH_1, SC_1.
pub mod prf_gs_4 {
    /// `provesIdentity` -> `GS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GS_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SC_5: O(1) resolution guarantee at saturation. Derived from SR_2 and FreeRank.isClosed at freeRank = 0.
pub mod prf_gs_5 {
    /// `provesIdentity` -> `GS_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GS_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SC_6: pre-reduction of effective budget. Derived from session-scoped site reduction at partial saturation.
pub mod prf_gs_6 {
    /// `provesIdentity` -> `GS_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GS_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SC_7: thermodynamic cooling cost. n site-closures at Landauer cost each via SR_1 + TH_4.
pub mod prf_gs_7 {
    /// `provesIdentity` -> `GS_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GS_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MS_1: connectivity lower bound β₀ ≥ 1. Formalisation of TS_7.
pub mod prf_ms_1 {
    /// `provesIdentity` -> `MS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MS_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MS_2: Euler capacity ceiling χ ≤ n. Derived from TS_1 constraint nerve dimension bound.
pub mod prf_ms_2 {
    /// `provesIdentity` -> `MS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MS_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MS_3: Betti monotonicity under constraint addition. Formalisation of TS_3.
pub mod prf_ms_3 {
    /// `provesIdentity` -> `MS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MS_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MS_4: level-relative achievability. Derived from WittLift construction (Amendment 29).
pub mod prf_ms_4 {
    /// `provesIdentity` -> `MS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MS_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MS_5: empirical completeness convergence. Convergence statement for verification accumulation.
pub mod prf_ms_5 {
    /// `provesIdentity` -> `MS_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MS_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of GD_1: geodesic condition. Dual condition from AR_1 ordering + DC_10 selection.
pub mod prf_gd_1 {
    /// `provesIdentity` -> `GD_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GD_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of GD_2: geodesic entropy bound. Each step on a geodesic erases exactly ln 2 nats.
pub mod prf_gd_2 {
    /// `provesIdentity` -> `GD_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GD_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of GD_3: total geodesic cost equals Landauer bound TH_4 with equality.
pub mod prf_gd_3 {
    /// `provesIdentity` -> `GD_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GD_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of GD_4: geodesic uniqueness up to step-order equivalence. Equal-J_k permutations are interchangeable.
pub mod prf_gd_4 {
    /// `provesIdentity` -> `GD_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GD_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of GD_5: subgeodesic detectability via step-by-step J_k check.
pub mod prf_gd_5 {
    /// `provesIdentity` -> `GD_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GD_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of QM_1: von Neumann–Landauer bridge. S_vN equals Landauer erasure cost at the Landauer temperature β* = ln 2.
pub mod prf_qm_1 {
    /// `provesIdentity` -> `QM_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QM_1";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of QM_2: measurement as site topology change. Projective collapse ≅ classical ResidueConstraint pinning.
pub mod prf_qm_2 {
    /// `provesIdentity` -> `QM_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QM_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of QM_3: superposition entropy bound. 0 ≤ S_vN ≤ ln 2 for single-site superpositions.
pub mod prf_qm_3 {
    /// `provesIdentity` -> `QM_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QM_3";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of QM_4: collapse idempotence. Re-measurement of a collapsed state is a no-op.
pub mod prf_qm_4 {
    /// `provesIdentity` -> `QM_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QM_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of QM_5: amplitude normalization (Born rule). Σ|αᵢ|² = 1 for well-formed SuperposedSiteState.
pub mod prf_qm_5 {
    /// `provesIdentity` -> `QM_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QM_5";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of RC_6: amplitude renormalization. Division by norm yields a normalized SuperposedSiteState.
pub mod prf_rc_6 {
    /// `provesIdentity` -> `RC_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RC_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of FPM_8: partition exhaustiveness. The four component cardinalities sum to 2ⁿ.
pub mod prf_fpm_8 {
    /// `provesIdentity` -> `FPM_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_8";
    /// `strategy` -> `DecideQ0`
    pub const STRATEGY: &str = "https://uor.foundation/proof/DecideQ0";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of FPM_9: exterior membership criterion. x ∈ Ext(T) iff x ∉ carrier(T).
pub mod prf_fpm_9 {
    /// `provesIdentity` -> `FPM_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FPM_9";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MN_8: holonomy classification covering. Every ConstrainedType is flat xor twisted.
pub mod prf_mn_8 {
    /// `provesIdentity` -> `MN_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MN_8";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of QL_8: quantum level chain inverse. wittLevelPredecessor is the left inverse of nextLevel.
pub mod prf_ql_8 {
    /// `provesIdentity` -> `QL_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QL_8";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of D_7: dihedral composition rule from the semidirect product presentation.
pub mod prf_d_7 {
    /// `provesIdentity` -> `D_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/D_7";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SP_1: classical embedding. Superposition resolution of a classical datum reduces to classical resolution.
pub mod prf_sp_1 {
    /// `provesIdentity` -> `SP_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SP_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SP_2: collapse–resolve commutativity. The collapse and resolve operations commute.
pub mod prf_sp_2 {
    /// `provesIdentity` -> `SP_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SP_2";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SP_3: amplitude preservation. The SuperpositionResolver preserves the normalized amplitude vector.
pub mod prf_sp_3 {
    /// `provesIdentity` -> `SP_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SP_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SP_4: Born rule outcome probability. P(collapse to site k) = |α_k|².
pub mod prf_sp_4 {
    /// `provesIdentity` -> `SP_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SP_4";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of PT_2a: product type partition tensor. Π(A × B) = PartitionProduct(Π(A), Π(B)).
pub mod prf_pt_2a {
    /// `provesIdentity` -> `PT_2a`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PT_2a";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of PT_2b: sum type partition coproduct. Π(A + B) = PartitionCoproduct(Π(A), Π(B)).
pub mod prf_pt_2b {
    /// `provesIdentity` -> `PT_2b`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PT_2b";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of GD_6: geodesic predicate decomposition. isGeodesic = isAR1Ordered ∧ isDC10Selected.
pub mod prf_gd_6 {
    /// `provesIdentity` -> `GD_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GD_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Impossibility witness for MS_1: β₀ = 0 is forbidden for any non-empty ConstrainedType because the constraint nerve is always connected.
pub mod iw_beta0_bound {
    /// `forbidsSignature`
    pub const FORBIDS_SIGNATURE: &str = "β₀ = 0";
    /// `impossibilityDomain` -> `Pipeline`
    pub const IMPOSSIBILITY_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
    /// `impossibilityReason`
    pub const IMPOSSIBILITY_REASON: &str =
        "β₀ = 0 violates MS_1: constraint nerve of non-empty set is connected";
    /// `strategy` -> `Contradiction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Contradiction";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Impossibility witness for MS_2: χ > n is forbidden at quantum level n. The Euler characteristic cannot exceed the quantum level.
pub mod iw_chi_ceiling {
    /// `forbidsSignature`
    pub const FORBIDS_SIGNATURE: &str = "χ > n";
    /// `impossibilityDomain` -> `Algebraic`
    pub const IMPOSSIBILITY_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
    /// `impossibilityReason`
    pub const IMPOSSIBILITY_REASON: &str =
        "χ > n violates MS_2: Euler characteristic bounded by quantum level";
    /// `strategy` -> `Contradiction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Contradiction";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Morphospace record: the IT_7d completeness target χ = n is achievable (sits at the ceiling of MS_2).
pub mod mr_completeness_target {
    /// `boundaryType` -> `Achievable`
    pub const BOUNDARY_TYPE: &str = "https://uor.foundation/observable/Achievable";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Morphospace record: the connectivity lower bound β₀ ≥ 1 marks the forbidden region from below.
pub mod mr_connectivity_lower {
    /// `boundaryType` -> `Forbidden`
    pub const BOUNDARY_TYPE: &str = "https://uor.foundation/observable/Forbidden";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of tower chain validity by induction on chain length.
pub mod prf_wt_1 {
    /// `baseCase` -> `prf_WLS_1`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WLS_1";
    /// `inductiveStep` -> `prf_WLS_6`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WLS_6";
    /// `provesIdentity` -> `WT_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_1";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of obstruction count bound: direct from QLS_2 localization.
pub mod prf_wt_2 {
    /// `provesIdentity` -> `WT_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of resolved basis size formula by induction on chain length.
pub mod prf_wt_3 {
    /// `baseCase` -> `prf_WT_3_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WT_3_base";
    /// `inductiveStep` -> `prf_WLS_3`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WLS_3";
    /// `provesIdentity` -> `WT_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_3";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of flat tower characterization: isFlat iff trivial holonomy at every step.
pub mod prf_wt_4 {
    /// `provesIdentity` -> `WT_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_4";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of LiftChainCertificate existence by induction on tower height.
pub mod prf_wt_5 {
    /// `baseCase` -> `prf_WT_5_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_WT_5_base";
    /// `inductiveStep` -> `prf_WT_1`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_WT_1";
    /// `provesIdentity` -> `WT_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_5";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of single-step reduction: QT_3 with chainLength=1 reduces to QLS_3.
pub mod prf_wt_6 {
    /// `provesIdentity` -> `WT_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_6";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of flat chain basis size formula.
pub mod prf_wt_7 {
    /// `provesIdentity` -> `WT_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_7";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CC_PINS: carry-constraint site-pinning map follows from ring carry propagation rule.
pub mod prf_cc_pins {
    /// `provesIdentity` -> `CC_PINS`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CC_PINS";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for CC_COST_SITE: exhaustive enumeration at Q0 confirms |pinsSites| = popcount + 1.
pub mod prf_cc_cost_site {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `CC_COST_SITE`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CC_COST_SITE";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of jsat_RR: CRT joint satisfiability follows from the Chinese Remainder Theorem.
pub mod prf_jsat_rr {
    /// `provesIdentity` -> `jsat_RR`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/jsat_RR";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of jsat_CR: carry-residue joint satisfiability follows from the carry stopping rule and residue class intersection.
pub mod prf_jsat_cr {
    /// `provesIdentity` -> `jsat_CR`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/jsat_CR";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for jsat_CC: bit-pattern exhaustive enumeration at Q0.
pub mod prf_jsat_cc {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `jsat_CC`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/jsat_CC";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of D_8: dihedral inverse formula follows from D_5 group presentation and D_7 composition rule.
pub mod prf_d_8 {
    /// `provesIdentity` -> `D_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/D_8";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of D_9: reflection order 2 follows from D_7 composition: (r^k s)(r^k s) = identity.
pub mod prf_d_9 {
    /// `provesIdentity` -> `D_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/D_9";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of EXP_1: monotone carrier characterization follows from site lattice monotonicity.
pub mod prf_exp_1 {
    /// `provesIdentity` -> `EXP_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EXP_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Computation certificate for EXP_2: principal filter count verified by exhaustive enumeration at Q0.
pub mod prf_exp_2 {
    /// `atWittLevel` -> `W8`
    pub const AT_WITT_LEVEL: &str = "https://uor.foundation/schema/W8";
    /// `provesIdentity` -> `EXP_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EXP_2";
    /// `strategy` -> `Computation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Computation";
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of EXP_3: SumType carrier is coproduct by definitional architectural decision.
pub mod prf_exp_3 {
    /// `provesIdentity` -> `EXP_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EXP_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_3: Euler characteristic additivity for disjoint simplicial complexes.
pub mod prf_st_3 {
    /// `provesIdentity` -> `ST_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_4: Betti number additivity via Mayer-Vietoris for disjoint union.
pub mod prf_st_4 {
    /// `provesIdentity` -> `ST_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_4";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_5: SumType completeness transfer follows from ST_3 + ST_4 + IT_7d.
pub mod prf_st_5 {
    /// `provesIdentity` -> `ST_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_5";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_6: unique existence of the PartitionCoproduct tag site. Follows from ST_2's single `ln 2` entropy quantum — distinguishing two variants requires exactly one bit, which fixes exactly one tag site logically disjoint from every data site of either operand.
pub mod prf_st_6 {
    /// `provesIdentity` -> `ST_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_7: PartitionCoproduct variant-tagging decomposition. constraints(A + B) = constraints(A) ∪ {tag=0} ∪ constraints(B) ∪ {tag=1}. Each tag-pinning constraint is emitted as an Affine with single-coefficient 1 at the tag site, distinguished by bias (0 for left, -1 for right).
pub mod prf_st_7 {
    /// `provesIdentity` -> `ST_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_8: variant nerve disjointness. The two tag-pinning constraints carry incompatible biases (0 vs -1) at the same tag site, so no single assignment satisfies both simultaneously. The variant nerves therefore share no common assignment — the bridge premise ST_3/ST_4 rely on.
pub mod prf_st_8 {
    /// `provesIdentity` -> `ST_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_8";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_9: χ additivity for PartitionCoproduct constructions. Combines ST_8's disjointness guarantee with the universal ST_3 (χ additive for any disjoint SumType).
pub mod prf_st_9 {
    /// `provesIdentity` -> `ST_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_9";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of ST_10: Betti additivity for PartitionCoproduct constructions. Combines ST_8's disjointness guarantee with the universal ST_4 (Betti additive at every dimension for any disjoint SumType).
pub mod prf_st_10 {
    /// `provesIdentity` -> `ST_10`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ST_10";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CPT_1: site additivity for Cartesian partition products. UOR sites are bit widths; |A ⊠ B| = 2^{n_A} · 2^{n_B} = 2^{n_A + n_B}, so sites add. Sister identity to PT_1 (same arithmetic; the two differ at the nerve-topology level per CPT_3 vs PT_3).
pub mod prf_cpt_1 {
    /// `provesIdentity` -> `CPT_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CPT_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CPT_2a: Π(A ⊠ B) = CartesianPartitionProduct(Π(A), Π(B)). Structural axiom defining the partition map on Cartesian-product types.
pub mod prf_cpt_2a {
    /// `provesIdentity` -> `CPT_2a`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CPT_2a";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CPT_3: χ multiplicativity for Cartesian partition products. Classical topology result — the simplicial product nerve has vertex set V(N(A)) × V(N(B)) and Euler characteristic χ(N(A)) · χ(N(B)). Distinguishes CartesianPartitionProduct from the site-disjoint-union PartitionProduct (which is χ-additive per PT_3).
pub mod prf_cpt_3 {
    /// `provesIdentity` -> `CPT_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CPT_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CPT_4: Künneth formula for Betti composition under Cartesian partition product. Follows from the classical Künneth theorem applied to the simplicial product nerve of the two component constraint systems.
pub mod prf_cpt_4 {
    /// `provesIdentity` -> `CPT_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CPT_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CPT_5: entropy additivity for Cartesian partition products. S(A ⊠ B) = S(A) + S(B) — Shannon additivity for independent subsystems. Consistent pointwise with IT_7a/b on the combined system.
pub mod prf_cpt_5 {
    /// `provesIdentity` -> `CPT_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CPT_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CPT_6: distributivity of Cartesian partition product over PartitionCoproduct. A ⊠ (B + C) ≡ (A ⊠ B) + (A ⊠ C) at the siteBudget, SITE_COUNT, χ, and entropy levels simultaneously. Does NOT extend to PartitionProduct (distribution over × duplicates the outer factor at the site-budget level).
pub mod prf_cpt_6 {
    /// `provesIdentity` -> `CPT_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CPT_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive proof of TS_8: minimum constraint count for beta_1 = k is 2k + 1. Base case at k=1 requires 3 mutually overlapping constraints.
pub mod prf_ts_8 {
    /// `baseCase` -> `prf_HA_1`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_HA_1";
    /// `inductiveStep` -> `prf_TS_4`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_TS_4";
    /// `provesIdentity` -> `TS_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_8";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 1;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive proof of TS_9: TypeSynthesisResolver terminates in at most 2^n steps. Base case at n=1 has 2 constraint combinations.
pub mod prf_ts_9 {
    /// `baseCase` -> `prf_TS_1`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_TS_1";
    /// `inductiveStep` -> `prf_TS_4`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_TS_4";
    /// `provesIdentity` -> `TS_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_9";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 1;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of TS_10: ForbiddenSignature membership follows from exhaustive enumeration bound.
pub mod prf_ts_10 {
    /// `provesIdentity` -> `TS_10`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TS_10";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of QT_8: ObstructionChain length bound follows from QLS_2 and spectral sequence convergence.
pub mod prf_wt_8 {
    /// `provesIdentity` -> `WT_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_8";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of QT_9: TowerCompletenessResolver termination follows from finite chain length and QT_8 bound.
pub mod prf_wt_9 {
    /// `provesIdentity` -> `WT_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WT_9";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of COEFF_1: Z/2Z coefficient ring is definitional, consistent with MN_7.
pub mod prf_coeff_1 {
    /// `provesIdentity` -> `COEFF_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/COEFF_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of GO_1: cohomology killing lemma for GluingObstruction feedback.
pub mod prf_go_1 {
    /// `provesIdentity` -> `GO_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GO_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SR_6: saturation re-entry free count follows from SR_1 monotone accumulation and SC_2.
pub mod prf_gr_6 {
    /// `provesIdentity` -> `GR_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SR_7: saturation degree degradation follows from SC_2 definition and SR_1 monotonicity.
pub mod prf_gr_7 {
    /// `provesIdentity` -> `GR_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Inductive proof of QM_6: amplitude index set equals monotone pinning trajectories. Base case at Q0 by exhaustive trajectory enumeration; inductive step by site lattice ordering.
pub mod prf_qm_6 {
    /// `baseCase` -> `prf_QM_6_base`
    pub const BASE_CASE: &str = "https://uor.foundation/proof/prf_QM_6_base";
    /// `inductiveStep` -> `prf_QM_6_step`
    pub const INDUCTIVE_STEP: &str = "https://uor.foundation/proof/prf_QM_6_step";
    /// `provesIdentity` -> `QM_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/QM_6";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `validForKAtLeast`
    pub const VALID_FOR_KAT_LEAST: i64 = 0;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CIC_1: TransformCertificate issuance coverage.
pub mod prf_cic_1 {
    /// `provesIdentity` -> `CIC_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CIC_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CIC_2: IsometryCertificate issuance coverage.
pub mod prf_cic_2 {
    /// `provesIdentity` -> `CIC_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CIC_2";
    /// `strategy` -> `GroupPresentation`
    pub const STRATEGY: &str = "https://uor.foundation/proof/GroupPresentation";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CIC_3: InvolutionCertificate issuance coverage.
pub mod prf_cic_3 {
    /// `provesIdentity` -> `CIC_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CIC_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CIC_4: GroundingCertificate issuance coverage.
pub mod prf_cic_4 {
    /// `provesIdentity` -> `CIC_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CIC_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CIC_5: GeodesicCertificate issuance coverage.
pub mod prf_cic_5 {
    /// `provesIdentity` -> `CIC_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CIC_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of CIC_6: MeasurementCertificate issuance coverage.
pub mod prf_cic_6 {
    /// `provesIdentity` -> `CIC_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CIC_6";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CIC_7: BornRuleVerification issuance coverage. Follows by composition from corrected OA_4 (product formula chain) and QM_5 (amplitude normalization).
pub mod prf_cic_7 {
    /// `provesIdentity` -> `CIC_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CIC_7";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of GC_1: GroundingCertificate issuance coverage.
pub mod prf_gc_1 {
    /// `provesIdentity` -> `GC_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GC_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SR_8: session composition tower consistency.
pub mod prf_gr_8 {
    /// `provesIdentity` -> `GR_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_8";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = false;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SR_9: ContextLease site disjointness.
pub mod prf_gr_9 {
    /// `provesIdentity` -> `GR_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_9";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of SR_10: ExecutionPolicy confluence.
pub mod prf_gr_10 {
    /// `provesIdentity` -> `GR_10`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GR_10";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MC_1: lease partition conserves total budget.
pub mod prf_mc_1 {
    /// `provesIdentity` -> `MC_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MC_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MC_2: per-lease binding monotonicity.
pub mod prf_mc_2 {
    /// `provesIdentity` -> `MC_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MC_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MC_3: composition freeRank inclusion-exclusion.
pub mod prf_mc_3 {
    /// `provesIdentity` -> `MC_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MC_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MC_4: disjoint-lease composition additivity.
pub mod prf_mc_4 {
    /// `provesIdentity` -> `MC_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MC_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MC_5: policy-invariant final binding set.
pub mod prf_mc_5 {
    /// `provesIdentity` -> `MC_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MC_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MC_6: full lease coverage implies composed saturation.
pub mod prf_mc_6 {
    /// `provesIdentity` -> `MC_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MC_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MC_7: distributed O(1) resolution.
pub mod prf_mc_7 {
    /// `provesIdentity` -> `MC_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MC_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Proof of MC_8: parallelism bound on per-session resolution work.
pub mod prf_mc_8 {
    /// `provesIdentity` -> `MC_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MC_8";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_1: Witt coordinate = bit coordinate at p=2.
pub mod prf_wc_1 {
    /// `provesIdentity` -> `WC_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_1";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_2: Witt sum correction = carry.
pub mod prf_wc_2 {
    /// `provesIdentity` -> `WC_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_2";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_3: carry recurrence = Witt polynomial recurrence.
pub mod prf_wc_3 {
    /// `provesIdentity` -> `WC_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_3";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_4: δ-correction = single-level carry.
pub mod prf_wc_4 {
    /// `provesIdentity` -> `WC_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_4";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_5: LiftObstruction = δ nonvanishing.
pub mod prf_wc_5 {
    /// `provesIdentity` -> `WC_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_5";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_6: metric discrepancy = Witt defect.
pub mod prf_wc_6 {
    /// `provesIdentity` -> `WC_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_6";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_7: D_1 = Witt truncation order.
pub mod prf_wc_7 {
    /// `provesIdentity` -> `WC_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_7";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_8: D_3 = Witt-Burnside conjugation.
pub mod prf_wc_8 {
    /// `provesIdentity` -> `WC_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_8";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_9: D_4 = reflection composition.
pub mod prf_wc_9 {
    /// `provesIdentity` -> `WC_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_9";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_10: Frobenius = identity on W_n(F_2).
pub mod prf_wc_10 {
    /// `provesIdentity` -> `WC_10`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_10";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_11: Verschiebung = doubling.
pub mod prf_wc_11 {
    /// `provesIdentity` -> `WC_11`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_11";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of WC_12: δ = squaring defect / 2.
pub mod prf_wc_12 {
    /// `provesIdentity` -> `WC_12`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/WC_12";
    /// `strategy` -> `BitwiseInduction`
    pub const STRATEGY: &str = "https://uor.foundation/proof/BitwiseInduction";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OA_1: Ostrowski product formula at p=2.
pub mod prf_oa_1 {
    /// `provesIdentity` -> `OA_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OA_1";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OA_2: crossing cost = ln 2.
pub mod prf_oa_2 {
    /// `provesIdentity` -> `OA_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OA_2";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OA_3: Landauer cost grounding via product formula.
pub mod prf_oa_3 {
    /// `provesIdentity` -> `OA_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OA_3";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OA_4: Born rule bridge follows from the product formula chain OA_1 (Ostrowski) -> OA_2 (crossing cost) -> OA_3 (Landauer grounding) -> OA_4.
pub mod prf_oa_4 {
    /// `provesIdentity` -> `OA_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OA_4";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OA_5: entropy per δ-level = crossing cost.
pub mod prf_oa_5 {
    /// `provesIdentity` -> `OA_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OA_5";
    /// `strategy` -> `ProductFormula`
    pub const STRATEGY: &str = "https://uor.foundation/proof/ProductFormula";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HT_1: the constraint nerve satisfies the Kan extension condition.
pub mod prf_ht_1 {
    /// `provesIdentity` -> `HT_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HT_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HT_2: path components recover Betti number β₀.
pub mod prf_ht_2 {
    /// `provesIdentity` -> `HT_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HT_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HT_3: π₁ factors through HolonomyGroup.
pub mod prf_ht_3 {
    /// `provesIdentity` -> `HT_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HT_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HT_4: higher homotopy groups vanish above dimension.
pub mod prf_ht_4 {
    /// `provesIdentity` -> `HT_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HT_4";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HT_5: 1-truncation determines flat/twisted classification.
pub mod prf_ht_5 {
    /// `provesIdentity` -> `HT_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HT_5";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HT_6: trivial k-invariants imply spectral collapse.
pub mod prf_ht_6 {
    /// `provesIdentity` -> `HT_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HT_6";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HT_7: Whitehead product detects lift obstructions.
pub mod prf_ht_7 {
    /// `provesIdentity` -> `HT_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HT_7";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HT_8: Hurewicz isomorphism for first non-vanishing group.
pub mod prf_ht_8 {
    /// `provesIdentity` -> `HT_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HT_8";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of ψ_7: KanComplex to PostnikovTower functor.
pub mod prf_psi_7 {
    /// `provesIdentity` -> `psi_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/psi_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of ψ_8: PostnikovTower to HomotopyGroups extraction.
pub mod prf_psi_8 {
    /// `provesIdentity` -> `psi_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/psi_8";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of ψ_9: HomotopyGroups to KInvariants computation.
pub mod prf_psi_9 {
    /// `provesIdentity` -> `psi_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/psi_9";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HP_1: pipeline composition ψ_7 ∘ ψ_1.
pub mod prf_hp_1 {
    /// `provesIdentity` -> `HP_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HP_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HP_2: homotopy extraction agrees with homology on truncation.
pub mod prf_hp_2 {
    /// `provesIdentity` -> `HP_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HP_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HP_3: ψ_9 detects QLS_4 convergence.
pub mod prf_hp_3 {
    /// `provesIdentity` -> `HP_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HP_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HP_4: HomotopyResolver complexity bound.
pub mod prf_hp_4 {
    /// `provesIdentity` -> `HP_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HP_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_1: moduli dimension equals basis cardinality.
pub mod prf_md_1 {
    /// `provesIdentity` -> `MD_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_2: automorphism group is subgroup of D_{2^n}.
pub mod prf_md_2 {
    /// `provesIdentity` -> `MD_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_3: first-order deformations parameterize tangent space.
pub mod prf_md_3 {
    /// `provesIdentity` -> `MD_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_4: obstruction space equals LiftObstruction.
pub mod prf_md_4 {
    /// `provesIdentity` -> `MD_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_4";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_5: FlatType stratum is open (codimension 0).
pub mod prf_md_5 {
    /// `provesIdentity` -> `MD_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_5";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_6: TwistedType strata have codimension at least 1.
pub mod prf_md_6 {
    /// `provesIdentity` -> `MD_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_6";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_7: versal deformation exists when unobstructed.
pub mod prf_md_7 {
    /// `provesIdentity` -> `MD_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_8: completeness-preserving iff obstruction vanishes along path.
pub mod prf_md_8 {
    /// `provesIdentity` -> `MD_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_8";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_9: tower map site dimension is 1 when unobstructed.
pub mod prf_md_9 {
    /// `provesIdentity` -> `MD_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_9";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MD_10: tower map site empty iff twisted at every level.
pub mod prf_md_10 {
    /// `provesIdentity` -> `MD_10`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MD_10";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MR_1: moduli resolver agrees with MorphospaceBoundary.
pub mod prf_mr_1 {
    /// `provesIdentity` -> `MR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MR_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MR_2: stratification record is complete.
pub mod prf_mr_2 {
    /// `provesIdentity` -> `MR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MR_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MR_3: moduli resolver complexity bound.
pub mod prf_mr_3 {
    /// `provesIdentity` -> `MR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MR_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MR_4: moduli-morphospace consistency.
pub mod prf_mr_4 {
    /// `provesIdentity` -> `MR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MR_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CY_1: carry generation condition.
pub mod prf_cy_1 {
    /// `provesIdentity` -> `CY_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CY_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CY_2: carry propagation condition.
pub mod prf_cy_2 {
    /// `provesIdentity` -> `CY_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CY_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CY_3: carry kill condition.
pub mod prf_cy_3 {
    /// `provesIdentity` -> `CY_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CY_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CY_4: d_Δ as carry–Hamming discrepancy.
pub mod prf_cy_4 {
    /// `provesIdentity` -> `CY_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CY_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CY_5: optimal encoding theorem.
pub mod prf_cy_5 {
    /// `provesIdentity` -> `CY_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CY_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CY_6: site ordering theorem.
pub mod prf_cy_6 {
    /// `provesIdentity` -> `CY_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CY_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CY_7: carry lookahead via prefix computation.
pub mod prf_cy_7 {
    /// `provesIdentity` -> `CY_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CY_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BM_1: saturation metric definition.
pub mod prf_bm_1 {
    /// `provesIdentity` -> `BM_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BM_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BM_2: Euler characteristic formula.
pub mod prf_bm_2 {
    /// `provesIdentity` -> `BM_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BM_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BM_3: index theorem linking all six metrics.
pub mod prf_bm_3 {
    /// `provesIdentity` -> `BM_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BM_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BM_4: Jacobian vanishes on pinned sites.
pub mod prf_bm_4 {
    /// `provesIdentity` -> `BM_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BM_4";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BM_5: d_delta equals Witt defect.
pub mod prf_bm_5 {
    /// `provesIdentity` -> `BM_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BM_5";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BM_6: metric composition tower.
pub mod prf_bm_6 {
    /// `provesIdentity` -> `BM_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BM_6";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of GL_1: σ as lower adjoint.
pub mod prf_gl_1 {
    /// `provesIdentity` -> `GL_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GL_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of GL_2: r as complement of upper adjoint.
pub mod prf_gl_2 {
    /// `provesIdentity` -> `GL_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GL_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of GL_3: completeness as Galois fixpoint.
pub mod prf_gl_3 {
    /// `provesIdentity` -> `GL_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GL_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of GL_4: Galois order reversal.
pub mod prf_gl_4 {
    /// `provesIdentity` -> `GL_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/GL_4";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of NV_1: nerve additivity for disjoint domains.
pub mod prf_nv_1 {
    /// `provesIdentity` -> `NV_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/NV_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of NV_2: Mayer–Vietoris for constraint nerves.
pub mod prf_nv_2 {
    /// `provesIdentity` -> `NV_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/NV_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of NV_3: Betti number bounded change.
pub mod prf_nv_3 {
    /// `provesIdentity` -> `NV_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/NV_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of NV_4: accumulation monotonicity.
pub mod prf_nv_4 {
    /// `provesIdentity` -> `NV_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/NV_4";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SD_1: scalar grounding identity.
pub mod prf_sd_1 {
    /// `provesIdentity` -> `SD_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SD_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SD_2: symbol grounding identity.
pub mod prf_sd_2 {
    /// `provesIdentity` -> `SD_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SD_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SD_3: sequence free monoid identity.
pub mod prf_sd_3 {
    /// `provesIdentity` -> `SD_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SD_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SD_4: tuple site additivity.
pub mod prf_sd_4 {
    /// `provesIdentity` -> `SD_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SD_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SD_5: graph nerve equality.
pub mod prf_sd_5 {
    /// `provesIdentity` -> `SD_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SD_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SD_6: set permutation invariance.
pub mod prf_sd_6 {
    /// `provesIdentity` -> `SD_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SD_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SD_7: tree acyclicity constraint.
pub mod prf_sd_7 {
    /// `provesIdentity` -> `SD_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SD_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SD_8: table functorial decomposition.
pub mod prf_sd_8 {
    /// `provesIdentity` -> `SD_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SD_8";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DD_1: dispatch determinism.
pub mod prf_dd_1 {
    /// `provesIdentity` -> `DD_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DD_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DD_2: dispatch coverage.
pub mod prf_dd_2 {
    /// `provesIdentity` -> `DD_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DD_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PI_1: inference idempotence.
pub mod prf_pi_1 {
    /// `provesIdentity` -> `PI_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PI_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PI_2: inference soundness.
pub mod prf_pi_2 {
    /// `provesIdentity` -> `PI_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PI_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PI_3: inference composition.
pub mod prf_pi_3 {
    /// `provesIdentity` -> `PI_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PI_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PI_4: inference complexity.
pub mod prf_pi_4 {
    /// `provesIdentity` -> `PI_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PI_4";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PI_5: inference coherence.
pub mod prf_pi_5 {
    /// `provesIdentity` -> `PI_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PI_5";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PA_1: accumulation permutation invariance.
pub mod prf_pa_1 {
    /// `provesIdentity` -> `PA_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PA_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PA_2: accumulation monotonicity.
pub mod prf_pa_2 {
    /// `provesIdentity` -> `PA_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PA_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PA_3: accumulation soundness.
pub mod prf_pa_3 {
    /// `provesIdentity` -> `PA_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PA_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PA_4: accumulation base preservation.
pub mod prf_pa_4 {
    /// `provesIdentity` -> `PA_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PA_4";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PA_5: accumulation identity element.
pub mod prf_pa_5 {
    /// `provesIdentity` -> `PA_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PA_5";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PL_1: lease disjointness.
pub mod prf_pl_1 {
    /// `provesIdentity` -> `PL_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PL_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PL_2: lease conservation.
pub mod prf_pl_2 {
    /// `provesIdentity` -> `PL_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PL_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PL_3: lease coverage.
pub mod prf_pl_3 {
    /// `provesIdentity` -> `PL_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PL_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PK_1: composition validity.
pub mod prf_pk_1 {
    /// `provesIdentity` -> `PK_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PK_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PK_2: distributed resolution.
pub mod prf_pk_2 {
    /// `provesIdentity` -> `PK_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PK_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PP_1: pipeline unification.
pub mod prf_pp_1 {
    /// `provesIdentity` -> `PP_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PP_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PE_1: state initialization.
pub mod prf_pe_1 {
    /// `provesIdentity` -> `PE_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PE_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PE_2: resolver dispatch.
pub mod prf_pe_2 {
    /// `provesIdentity` -> `PE_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PE_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PE_3: ring address grounding.
pub mod prf_pe_3 {
    /// `provesIdentity` -> `PE_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PE_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PE_4: constraint resolution.
pub mod prf_pe_4 {
    /// `provesIdentity` -> `PE_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PE_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PE_5: consistent accumulation.
pub mod prf_pe_5 {
    /// `provesIdentity` -> `PE_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PE_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PE_6: coherent extraction.
pub mod prf_pe_6 {
    /// `provesIdentity` -> `PE_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PE_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PE_7: full pipeline composition.
pub mod prf_pe_7 {
    /// `provesIdentity` -> `PE_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PE_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PM_1: phase rotation.
pub mod prf_pm_1 {
    /// `provesIdentity` -> `PM_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PM_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PM_2: phase gate check.
pub mod prf_pm_2 {
    /// `provesIdentity` -> `PM_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PM_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PM_3: conjugate rollback.
pub mod prf_pm_3 {
    /// `provesIdentity` -> `PM_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PM_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PM_4: rollback involution.
pub mod prf_pm_4 {
    /// `provesIdentity` -> `PM_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PM_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PM_5: epoch saturation preservation.
pub mod prf_pm_5 {
    /// `provesIdentity` -> `PM_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PM_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PM_6: service window context.
pub mod prf_pm_6 {
    /// `provesIdentity` -> `PM_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PM_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PM_7: machine determinism.
pub mod prf_pm_7 {
    /// `provesIdentity` -> `PM_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PM_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of ER_1: guard satisfaction.
pub mod prf_er_1 {
    /// `provesIdentity` -> `ER_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ER_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of ER_2: effect atomicity.
pub mod prf_er_2 {
    /// `provesIdentity` -> `ER_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ER_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of ER_3: guard purity.
pub mod prf_er_3 {
    /// `provesIdentity` -> `ER_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ER_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of ER_4: intra-stage commutativity.
pub mod prf_er_4 {
    /// `provesIdentity` -> `ER_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/ER_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EA_1: epoch boundary reset.
pub mod prf_ea_1 {
    /// `provesIdentity` -> `EA_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EA_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EA_2: saturation monotonicity.
pub mod prf_ea_2 {
    /// `provesIdentity` -> `EA_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EA_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EA_3: service window bound.
pub mod prf_ea_3 {
    /// `provesIdentity` -> `EA_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EA_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EA_4: epoch admission exclusivity.
pub mod prf_ea_4 {
    /// `provesIdentity` -> `EA_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EA_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OE_1: stage fusion.
pub mod prf_oe_1 {
    /// `provesIdentity` -> `OE_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OE_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OE_2: effect commutativity.
pub mod prf_oe_2 {
    /// `provesIdentity` -> `OE_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OE_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OE_3: lease parallelism.
pub mod prf_oe_3 {
    /// `provesIdentity` -> `OE_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OE_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OE_4a: fusion semantics preservation.
pub mod prf_oe_4a {
    /// `provesIdentity` -> `OE_4a`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OE_4a";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OE_4b: commutation outcome preservation.
pub mod prf_oe_4b {
    /// `provesIdentity` -> `OE_4b`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OE_4b";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OE_4c: parallelism coverage preservation.
pub mod prf_oe_4c {
    /// `provesIdentity` -> `OE_4c`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OE_4c";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CS_1: bounded stage cost.
pub mod prf_cs_1 {
    /// `provesIdentity` -> `CS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CS_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CS_2: additive pipeline cost.
pub mod prf_cs_2 {
    /// `provesIdentity` -> `CS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CS_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CS_3: bounded rollback cost.
pub mod prf_cs_3 {
    /// `provesIdentity` -> `CS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CS_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CS_4: constant preflight cost.
pub mod prf_cs_4 {
    /// `provesIdentity` -> `CS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CS_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CS_5: total reduction cost bound.
pub mod prf_cs_5 {
    /// `provesIdentity` -> `CS_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CS_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FA_1: query liveness.
pub mod prf_fa_1 {
    /// `provesIdentity` -> `FA_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FA_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FA_2: no starvation.
pub mod prf_fa_2 {
    /// `provesIdentity` -> `FA_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FA_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FA_3: fair lease allocation.
pub mod prf_fa_3 {
    /// `provesIdentity` -> `FA_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FA_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SW_1: memory boundedness.
pub mod prf_sw_1 {
    /// `provesIdentity` -> `SW_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SW_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SW_2: saturation invariance.
pub mod prf_sw_2 {
    /// `provesIdentity` -> `SW_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SW_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SW_3: eviction releases resources.
pub mod prf_sw_3 {
    /// `provesIdentity` -> `SW_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SW_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SW_4: non-empty window.
pub mod prf_sw_4 {
    /// `provesIdentity` -> `SW_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SW_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LS_1: suspension preserves pinned state.
pub mod prf_ls_1 {
    /// `provesIdentity` -> `LS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LS_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LS_2: expiry releases resources.
pub mod prf_ls_2 {
    /// `provesIdentity` -> `LS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LS_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LS_3: checkpoint restore idempotence.
pub mod prf_ls_3 {
    /// `provesIdentity` -> `LS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LS_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LS_4: suspend-resume round-trip.
pub mod prf_ls_4 {
    /// `provesIdentity` -> `LS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LS_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TJ_1: AllOrNothing rollback.
pub mod prf_tj_1 {
    /// `provesIdentity` -> `TJ_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TJ_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TJ_2: BestEffort partial commit.
pub mod prf_tj_2 {
    /// `provesIdentity` -> `TJ_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TJ_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of TJ_3: epoch-scoped atomicity.
pub mod prf_tj_3 {
    /// `provesIdentity` -> `TJ_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/TJ_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AP_1: saturation monotonicity.
pub mod prf_ap_1 {
    /// `provesIdentity` -> `AP_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AP_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AP_2: quality improvement.
pub mod prf_ap_2 {
    /// `provesIdentity` -> `AP_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AP_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AP_3: deferred query liveness.
pub mod prf_ap_3 {
    /// `provesIdentity` -> `AP_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AP_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EC_1: phase half-turn convergence.
pub mod prf_ec_1 {
    /// `provesIdentity` -> `EC_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EC_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EC_2: conjugate involution.
pub mod prf_ec_2 {
    /// `provesIdentity` -> `EC_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EC_2";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EC_3: pairwise commutator convergence.
pub mod prf_ec_3 {
    /// `provesIdentity` -> `EC_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EC_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EC_4: triple associator convergence.
pub mod prf_ec_4 {
    /// `provesIdentity` -> `EC_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EC_4";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EC_4a: associator monotonicity.
pub mod prf_ec_4a {
    /// `provesIdentity` -> `EC_4a`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EC_4a";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EC_4b: associator finiteness.
pub mod prf_ec_4b {
    /// `provesIdentity` -> `EC_4b`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EC_4b";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EC_4c: vanishing implies associativity.
pub mod prf_ec_4c {
    /// `provesIdentity` -> `EC_4c`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EC_4c";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of EC_5: Adams termination.
pub mod prf_ec_5 {
    /// `provesIdentity` -> `EC_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/EC_5";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DA_1: Cayley-Dickson R→C.
pub mod prf_da_1 {
    /// `provesIdentity` -> `DA_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DA_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DA_2: Cayley-Dickson C→H.
pub mod prf_da_2 {
    /// `provesIdentity` -> `DA_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DA_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DA_3: Cayley-Dickson H→O.
pub mod prf_da_3 {
    /// `provesIdentity` -> `DA_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DA_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DA_4: Adams dimension restriction.
pub mod prf_da_4 {
    /// `provesIdentity` -> `DA_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DA_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DA_5: convergence-level algebra correspondence.
pub mod prf_da_5 {
    /// `provesIdentity` -> `DA_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DA_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DA_6: commutator-commutativity equivalence.
pub mod prf_da_6 {
    /// `provesIdentity` -> `DA_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DA_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DA_7: associator-associativity equivalence.
pub mod prf_da_7 {
    /// `provesIdentity` -> `DA_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DA_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_1: interaction cost.
pub mod prf_in_1 {
    /// `provesIdentity` -> `IN_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_2: disjoint leases commute.
pub mod prf_in_2 {
    /// `provesIdentity` -> `IN_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_3: shared sites nonzero commutator.
pub mod prf_in_3 {
    /// `provesIdentity` -> `IN_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_4: negotiation convergence.
pub mod prf_in_4 {
    /// `provesIdentity` -> `IN_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_4";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_5: commutative subspace selection.
pub mod prf_in_5 {
    /// `provesIdentity` -> `IN_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_5";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_6: pairwise outcome space.
pub mod prf_in_6 {
    /// `provesIdentity` -> `IN_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_6";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_7: associative subalgebra selection.
pub mod prf_in_7 {
    /// `provesIdentity` -> `IN_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_7";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_8: nerve Betti coupling bound.
pub mod prf_in_8 {
    /// `provesIdentity` -> `IN_8`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_8";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IN_9: Betti-disagreement associator bound.
pub mod prf_in_9 {
    /// `provesIdentity` -> `IN_9`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IN_9";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AS_1: δ-ι-κ non-associativity.
pub mod prf_as_1 {
    /// `provesIdentity` -> `AS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AS_1";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AS_2: ι-α-λ non-associativity.
pub mod prf_as_2 {
    /// `provesIdentity` -> `AS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AS_2";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AS_3: λ-κ-δ non-associativity.
pub mod prf_as_3 {
    /// `provesIdentity` -> `AS_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AS_3";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of AS_4: non-associativity root cause.
pub mod prf_as_4 {
    /// `provesIdentity` -> `AS_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/AS_4";
    /// `strategy` -> `Composition`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Composition";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MO_1: monoidal unit law.
pub mod prf_mo_1 {
    /// `provesIdentity` -> `MO_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MO_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MO_2: monoidal associativity.
pub mod prf_mo_2 {
    /// `provesIdentity` -> `MO_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MO_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MO_3: certificate composition.
pub mod prf_mo_3 {
    /// `provesIdentity` -> `MO_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MO_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MO_4: saturation monotonicity.
pub mod prf_mo_4 {
    /// `provesIdentity` -> `MO_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MO_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of MO_5: residual monotonicity.
pub mod prf_mo_5 {
    /// `provesIdentity` -> `MO_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/MO_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OP_1: site additivity.
pub mod prf_op_1 {
    /// `provesIdentity` -> `OP_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OP_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OP_2: grounding distributivity.
pub mod prf_op_2 {
    /// `provesIdentity` -> `OP_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OP_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OP_3: d_Δ decomposition.
pub mod prf_op_3 {
    /// `provesIdentity` -> `OP_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OP_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OP_4: tabular data decomposition.
pub mod prf_op_4 {
    /// `provesIdentity` -> `OP_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OP_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of OP_5: hierarchical data structure.
pub mod prf_op_5 {
    /// `provesIdentity` -> `OP_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/OP_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FX_1: pinning site budget decrement.
pub mod prf_fx_1 {
    /// `provesIdentity` -> `FX_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FX_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FX_2: unbinding site budget increment.
pub mod prf_fx_2 {
    /// `provesIdentity` -> `FX_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FX_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FX_3: phase budget invariance.
pub mod prf_fx_3 {
    /// `provesIdentity` -> `FX_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FX_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FX_4: disjoint commutativity.
pub mod prf_fx_4 {
    /// `provesIdentity` -> `FX_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FX_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FX_5: composite delta additivity.
pub mod prf_fx_5 {
    /// `provesIdentity` -> `FX_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FX_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FX_6: reversible inverse.
pub mod prf_fx_6 {
    /// `provesIdentity` -> `FX_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FX_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FX_7: external shape compliance.
pub mod prf_fx_7 {
    /// `provesIdentity` -> `FX_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FX_7";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PR_1: predicate totality.
pub mod prf_pr_1 {
    /// `provesIdentity` -> `PR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PR_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PR_2: predicate purity.
pub mod prf_pr_2 {
    /// `provesIdentity` -> `PR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PR_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PR_3: deterministic dispatch.
pub mod prf_pr_3 {
    /// `provesIdentity` -> `PR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PR_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PR_4: deterministic match.
pub mod prf_pr_4 {
    /// `provesIdentity` -> `PR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PR_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PR_5: typed guard transition.
pub mod prf_pr_5 {
    /// `provesIdentity` -> `PR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PR_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CG_1: typed entry guard.
pub mod prf_cg_1 {
    /// `provesIdentity` -> `CG_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CG_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CG_2: typed exit guard with effect.
pub mod prf_cg_2 {
    /// `provesIdentity` -> `CG_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CG_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DIS_1: exhaustive exclusive table.
pub mod prf_dis_1 {
    /// `provesIdentity` -> `DIS_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DIS_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of DIS_2: deterministic resolver selection.
pub mod prf_dis_2 {
    /// `provesIdentity` -> `DIS_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/DIS_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PAR_1: disjoint commutativity.
pub mod prf_par_1 {
    /// `provesIdentity` -> `PAR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PAR_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PAR_2: delta additivity.
pub mod prf_par_2 {
    /// `provesIdentity` -> `PAR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PAR_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PAR_3: exhaustive partitioning.
pub mod prf_par_3 {
    /// `provesIdentity` -> `PAR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PAR_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PAR_4: interleaving invariance.
pub mod prf_par_4 {
    /// `provesIdentity` -> `PAR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PAR_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of PAR_5: certificate conjunction.
pub mod prf_par_5 {
    /// `provesIdentity` -> `PAR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/PAR_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HO_1: content-addressed certification.
pub mod prf_ho_1 {
    /// `provesIdentity` -> `HO_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HO_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HO_2: application certification.
pub mod prf_ho_2 {
    /// `provesIdentity` -> `HO_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HO_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HO_3: composition certification.
pub mod prf_ho_3 {
    /// `provesIdentity` -> `HO_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HO_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of HO_4: saturation equivalence.
pub mod prf_ho_4 {
    /// `provesIdentity` -> `HO_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/HO_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of STR_1: epoch termination.
pub mod prf_str_1 {
    /// `provesIdentity` -> `STR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/STR_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of STR_2: saturation preservation.
pub mod prf_str_2 {
    /// `provesIdentity` -> `STR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/STR_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of STR_3: finite prefix computability.
pub mod prf_str_3 {
    /// `provesIdentity` -> `STR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/STR_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of STR_4: unfold seed initialization.
pub mod prf_str_4 {
    /// `provesIdentity` -> `STR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/STR_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of STR_5: continuation chaining.
pub mod prf_str_5 {
    /// `provesIdentity` -> `STR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/STR_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of STR_6: lease expiry budget return.
pub mod prf_str_6 {
    /// `provesIdentity` -> `STR_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/STR_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FLR_1: coproduct exhaustiveness.
pub mod prf_flr_1 {
    /// `provesIdentity` -> `FLR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FLR_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FLR_2: total computation guarantee.
pub mod prf_flr_2 {
    /// `provesIdentity` -> `FLR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FLR_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FLR_3: sequential propagation.
pub mod prf_flr_3 {
    /// `provesIdentity` -> `FLR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FLR_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FLR_4: parallel independence.
pub mod prf_flr_4 {
    /// `provesIdentity` -> `FLR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FLR_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FLR_5: recovery result.
pub mod prf_flr_5 {
    /// `provesIdentity` -> `FLR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FLR_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of FLR_6: conjugate rollback.
pub mod prf_flr_6 {
    /// `provesIdentity` -> `FLR_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/FLR_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LN_1: exact coverage.
pub mod prf_ln_1 {
    /// `provesIdentity` -> `LN_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LN_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LN_2: pinning effect.
pub mod prf_ln_2 {
    /// `provesIdentity` -> `LN_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LN_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LN_3: consumption linearity.
pub mod prf_ln_3 {
    /// `provesIdentity` -> `LN_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LN_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LN_4: lease budget decrement.
pub mod prf_ln_4 {
    /// `provesIdentity` -> `LN_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LN_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LN_5: lease expiry return.
pub mod prf_ln_5 {
    /// `provesIdentity` -> `LN_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LN_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of LN_6: geodesic linearity.
pub mod prf_ln_6 {
    /// `provesIdentity` -> `LN_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/LN_6";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SB_1: constraint superset.
pub mod prf_sb_1 {
    /// `provesIdentity` -> `SB_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SB_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SB_2: resolution subset.
pub mod prf_sb_2 {
    /// `provesIdentity` -> `SB_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SB_2";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SB_3: nerve sub-complex.
pub mod prf_sb_3 {
    /// `provesIdentity` -> `SB_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SB_3";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SB_4: covariance.
pub mod prf_sb_4 {
    /// `provesIdentity` -> `SB_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SB_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SB_5: contravariance.
pub mod prf_sb_5 {
    /// `provesIdentity` -> `SB_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SB_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of SB_6: lattice depth.
pub mod prf_sb_6 {
    /// `provesIdentity` -> `SB_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/SB_6";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BR_1: strict descent.
pub mod prf_br_1 {
    /// `provesIdentity` -> `BR_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BR_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BR_2: depth bound.
pub mod prf_br_2 {
    /// `provesIdentity` -> `BR_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BR_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BR_3: termination guarantee.
pub mod prf_br_3 {
    /// `provesIdentity` -> `BR_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BR_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BR_4: structural measure.
pub mod prf_br_4 {
    /// `provesIdentity` -> `BR_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BR_4";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of BR_5: base predicate zero.
pub mod prf_br_5 {
    /// `provesIdentity` -> `BR_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/BR_5";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RG_1: nerve-determined working set.
pub mod prf_rg_1 {
    /// `provesIdentity` -> `RG_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RG_1";
    /// `strategy` -> `EulerPoincare`
    pub const STRATEGY: &str = "https://uor.foundation/proof/EulerPoincare";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RG_2: diameter bound.
pub mod prf_rg_2 {
    /// `provesIdentity` -> `RG_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RG_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RG_3: addressable space bound.
pub mod prf_rg_3 {
    /// `provesIdentity` -> `RG_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RG_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of RG_4: working set containment.
pub mod prf_rg_4 {
    /// `provesIdentity` -> `RG_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/RG_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IO_1: ingest type conformance.
pub mod prf_io_1 {
    /// `provesIdentity` -> `IO_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IO_1";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IO_2: emit type conformance.
pub mod prf_io_2 {
    /// `provesIdentity` -> `IO_2`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IO_2";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IO_3: grounding validity.
pub mod prf_io_3 {
    /// `provesIdentity` -> `IO_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IO_3";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IO_4: projection validity.
pub mod prf_io_4 {
    /// `provesIdentity` -> `IO_4`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IO_4";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IO_5: non-vacuous crossing.
pub mod prf_io_5 {
    /// `provesIdentity` -> `IO_5`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IO_5";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CS_6: budget solvency rejection.
pub mod prf_cs_6 {
    /// `provesIdentity` -> `CS_6`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CS_6";
    /// `strategy` -> `Simplification`
    pub const STRATEGY: &str = "https://uor.foundation/proof/Simplification";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of CS_7: unit address computation.
pub mod prf_cs_7 {
    /// `provesIdentity` -> `CS_7`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/CS_7";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Axiomatic derivation of IH_1 (inhabitance soundness): cert:InhabitanceCertificate(T).verified iff carrier(T) ≠ ∅.
pub mod prf_ih_1 {
    /// `provesIdentity` -> `IH_1`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IH_1";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Cost identity for the 2-SAT decider on Is2SatShape instances. Inherited from the classical 2-SAT polynomial decision procedure.
pub mod prf_ih_2a {
    /// `provesIdentity` -> `IH_2a`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IH_2a";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Cost identity for the Horn-SAT decider on IsHornShape instances. Inherited from the classical Horn-SAT polynomial decision procedure via unit propagation.
pub mod prf_ih_2b {
    /// `provesIdentity` -> `IH_2b`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IH_2b";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}

/// Carrier preservation under basis reduction. Discharged against resolver:JacobianGuidedResolver and resolver:guidingJacobian vocabulary.
pub mod prf_ih_3 {
    /// `provesIdentity` -> `IH_3`
    pub const PROVES_IDENTITY: &str = "https://uor.foundation/op/IH_3";
    /// `strategy` -> `RingAxiom`
    pub const STRATEGY: &str = "https://uor.foundation/proof/RingAxiom";
    /// `universalScope`
    pub const UNIVERSAL_SCOPE: bool = true;
    /// `verified`
    pub const VERIFIED: bool = true;
}