uor_foundation/kernel/

op.rs

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

//! `op/` namespace — Ring operations, involutions, algebraic identities, and the dihedral symmetry group D_{2^n} generated by neg and bnot..
//!
//! Space: Kernel

use crate::enums::GeometricCharacter;
use crate::enums::ValidityScopeKind;
use crate::enums::VerificationDomain;
use crate::enums::WittLevel;
use crate::HostTypes;

/// An operation on the ring Z/(2^n)Z. The root class for all UOR kernel operations.
pub trait Operation<H: HostTypes> {
    /// The number of arguments this operation takes. 1 for unary operations, 2 for binary operations.
    fn arity(&self) -> u64;
    /// The geometric role of this operation in the UOR ring and hypercube geometry. Functional: each operation has exactly one geometric character.
    fn has_geometric_character(&self) -> GeometricCharacter;
    /// Associated type for `Operation`.
    type OperationTarget: Operation<H>;
    /// The inverse operation: the operation inv_op such that op(x, inv_op(x)) = e for all x, where e is the identity.
    fn inverse(&self) -> &Self::OperationTarget;
    /// Ordered list of operations this operation is composed from. Uses rdf:List to preserve application order (first element applied innermost). E.g., succ = neg ∘ bnot is encoded as \[op:neg, op:bnot\] meaning neg applied to the result of bnot.
    fn composed_of(&self) -> &H::HostString;
    /// True iff this Operation participates in the Z/(2^n)Z ring-arithmetic vocabulary. Annotation drives the Lean RingOp class generation in UOR/Enforcement.lean.
    fn is_ring_op(&self) -> bool;
}

/// A unary operation on the ring: takes one datum and produces one datum.
pub trait UnaryOp<H: HostTypes>: Operation<H> {}

/// A binary operation on the ring: takes two datums and produces one datum.
pub trait BinaryOp<H: HostTypes>: Operation<H> {
    /// Whether this binary operation satisfies op(x,y) = op(y,x) for all x, y in R_n.
    fn commutative(&self) -> bool;
    /// Whether this binary operation satisfies op(op(x,y),z) = op(x,op(y,z)) for all x, y, z in R_n.
    fn associative(&self) -> bool;
    /// The identity element of this binary operation: the value e such that op(x, e) = op(e, x) = x for all x in R_n.
    fn identity(&self) -> i64;
}

/// A unary operation f such that f(f(x)) = x for all x in R_n. The two UOR involutions are neg (ring reflection) and bnot (hypercube reflection).
pub trait Involution<H: HostTypes>: UnaryOp<H> {}

/// An algebraic identity: a statement that two expressions are equal for all inputs. The critical identity is neg(bnot(x)) = succ(x) for all x in R_n.
pub trait Identity<H: HostTypes> {
    /// Associated type for `TermExpression`.
    type TermExpression: crate::kernel::schema::TermExpression<H>;
    /// The left-hand side of an algebraic identity as a typed AST node (schema:TermExpression).
    fn lhs(&self) -> &Self::TermExpression;
    /// The right-hand side of an algebraic identity as a typed AST node (schema:TermExpression).
    fn rhs(&self) -> &Self::TermExpression;
    /// Associated type for `ForAllDeclaration`.
    type ForAllDeclaration: crate::kernel::schema::ForAllDeclaration<H>;
    /// The quantifier scope: a typed declaration of the variable(s) over which this identity holds.
    fn for_all(&self) -> &Self::ForAllDeclaration;
    /// The mathematical discipline(s) through which this identity is established. Range is op:VerificationDomain. Non-functional: composite identities (e.g. IT_7a–IT_7d) reference multiple domain individuals.
    fn verification_domain(&self) -> &[VerificationDomain];
    /// Associated type for `WittLevelBinding`.
    type WittLevelBinding: WittLevelBinding<H>;
    /// Links an Identity individual to a WittLevelBinding attesting verification at a specific quantum level. Non-functional: one binding per (Identity, WittLevel) pair.
    fn verified_at_level(&self) -> &[Self::WittLevelBinding];
    /// True iff this identity holds for all n ≥ 1 (proved symbolically by induction on the ring axioms, not just exhaustively at Q0). Identities that reference 8-bit-specific constants receive universallyValid = false.
    fn universally_valid(&self) -> bool;
    /// The structured validity scope of this identity, replacing the binary universallyValid flag. Required on all new Identity individuals.
    fn validity_kind(&self) -> ValidityScopeKind;
    /// Minimum quantum level index k for ParametricLower and ParametricRange scopes.
    fn valid_kmin(&self) -> u64;
    /// Maximum quantum level index k (inclusive) for ParametricRange scope.
    fn valid_kmax(&self) -> u64;
}

/// A group: a set with an associative binary operation, an identity element, and inverses for every element.
pub trait Group<H: HostTypes> {
    /// Associated type for `Operation`.
    type Operation: Operation<H>;
    /// An operation that generates this group. The dihedral group D_{2^n} is generated by op:neg and op:bnot.
    fn generated_by(&self) -> &[Self::Operation];
    /// The number of elements in the group. For D_{2^n}, the order is 2^(n+1).
    fn order(&self) -> u64;
}

/// The dihedral group D_{2^n} of order 2^(n+1), generated by the ring reflection (neg) and the hypercube reflection (bnot). This group governs the symmetry of the UOR type space.
pub trait DihedralGroup<H: HostTypes>: Group<H> {}

/// A record linking an op:Identity individual to a specific quantum level at which it has been verified. Non-functional: one WittLevelBinding per (Identity, WittLevel) pair verified.
pub trait WittLevelBinding<H: HostTypes> {
    /// The quantum level at which this WittLevelBinding was verified.
    fn binding_level(&self) -> WittLevel;
}

/// A verification domain at the intersection of quantum superposition and classical thermodynamics. Identities in this domain require both SuperpositionDomain and Thermodynamic reasoning simultaneously.
pub trait QuantumThermodynamicDomain<H: HostTypes> {}

/// An operation formed by composing ring operations, witnessed by op:composedOf and morphism/CompositionLaw.
pub trait ComposedOperation<H: HostTypes>:
    Operation<H> + crate::user::morphism::Composition<H>
{
    /// Associated type for `Operation`.
    type Operation: Operation<H>;
    /// References a constituent operation of a ComposedOperation. Non-functional: a composed operation may reference multiple constituent operations.
    fn composed_of_ops(&self) -> &[Self::Operation];
    /// Associated type for `TypeDefinition`.
    type TypeDefinition: crate::user::type_::TypeDefinition<H>;
    /// The domain type of a composed operation.
    fn operator_domain_type(&self) -> &Self::TypeDefinition;
    /// The range type of a composed operation.
    fn operator_range_type(&self) -> &Self::TypeDefinition;
    /// The computational complexity class of a composed operation.
    fn operator_complexity(&self) -> &H::HostString;
    /// Whether this composed operation is idempotent.
    fn operator_idempotent(&self) -> bool;
    /// The number of constituent operations in a composed operation.
    fn composed_operator_count(&self) -> u64;
    /// Whether applying this operation twice yields the identity.
    fn is_involutory(&self) -> bool;
    /// Associated type for `TermExpression`.
    type TermExpression: crate::kernel::schema::TermExpression<H>;
    /// Description of the convergence guarantee for this operation.
    fn convergence_guarantee(&self) -> &Self::TermExpression;
}

/// δ: Query × ResolverRegistry → Resolver. Non-commutative, non-associative, arity 2.
pub trait DispatchOperation<H: HostTypes>: ComposedOperation<H> {
    /// The source selector for a dispatch operation.
    fn dispatch_source(&self) -> &Self::Operation;
    /// The target resolver for a dispatch operation.
    fn dispatch_target(&self) -> &Self::Operation;
}

/// ι = P ∘ Π ∘ G (the φ-pipeline composed). Non-commutative, non-associative, arity 2.
pub trait InferenceOperation<H: HostTypes>: ComposedOperation<H> {
    /// The source data for an inference operation.
    fn inference_source(&self) -> &Self::Operation;
    /// The target type for an inference operation.
    fn inference_target(&self) -> &Self::Operation;
    /// The pipeline through which inference is performed.
    fn inference_pipeline(&self) -> &Self::Operation;
}

/// α: Binding × Context → Context. Non-commutative, associative at convergence (SR_10), arity 2.
pub trait AccumulationOperation<H: HostTypes>: ComposedOperation<H> {
    /// The base value for an accumulation operation.
    fn accumulation_base(&self) -> &Self::TermExpression;
    /// The binding accumulator for an accumulation operation.
    fn accumulation_binding(&self) -> &Self::TermExpression;
}

/// λ: SharedContext × ℕ → ContextLease^k. Non-commutative, non-associative, arity 2.
pub trait LeasePartitionOperation<H: HostTypes>: ComposedOperation<H> {
    /// The source context for a lease partition operation.
    fn lease_source(&self) -> &Self::Operation;
    /// The partition factor for a lease partition operation.
    fn lease_factor(&self) -> &Self::Operation;
    /// The number of partitions in a lease partition operation.
    fn lease_partition_count(&self) -> u64;
}

/// κ: Session × Session → Session. Commutative (disjoint leases), associative (SR_8), arity 2.
pub trait SessionCompositionOperation<H: HostTypes>: ComposedOperation<H> {
    /// The left session in a session composition operation.
    fn composition_left_session(&self) -> &Self::Operation;
    /// The right session in a session composition operation.
    fn composition_right_session(&self) -> &Self::Operation;
}

/// A structured group presentation: generators and relations as typed data rather than prose strings.
pub trait GroupPresentation<H: HostTypes> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `Operation<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 NullOperation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullOperation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullOperation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullOperation<H> = NullOperation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullOperation<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `UnaryOp<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 NullUnaryOp<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullUnaryOp<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullUnaryOp<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullUnaryOp<H> = NullUnaryOp {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullUnaryOp<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> UnaryOp<H> for NullUnaryOp<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `BinaryOp<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 NullBinaryOp<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullBinaryOp<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullBinaryOp<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullBinaryOp<H> = NullBinaryOp {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullBinaryOp<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> BinaryOp<H> for NullBinaryOp<H> {
    fn commutative(&self) -> bool {
        false
    }
    fn associative(&self) -> bool {
        false
    }
    fn identity(&self) -> i64 {
        0
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `Involution<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 NullInvolution<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullInvolution<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullInvolution<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullInvolution<H> = NullInvolution {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullInvolution<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> UnaryOp<H> for NullInvolution<H> {}
impl<H: HostTypes> Involution<H> for NullInvolution<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `Identity<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 NullIdentity<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullIdentity<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullIdentity<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullIdentity<H> = NullIdentity {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Identity<H> for NullIdentity<H> {
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn lhs(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
    fn rhs(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
    type ForAllDeclaration = crate::kernel::schema::NullForAllDeclaration<H>;
    fn for_all(&self) -> &Self::ForAllDeclaration {
        &<crate::kernel::schema::NullForAllDeclaration<H>>::ABSENT
    }
    fn verification_domain(&self) -> &[VerificationDomain] {
        &[]
    }
    type WittLevelBinding = NullWittLevelBinding<H>;
    fn verified_at_level(&self) -> &[Self::WittLevelBinding] {
        &[]
    }
    fn universally_valid(&self) -> bool {
        false
    }
    fn validity_kind(&self) -> ValidityScopeKind {
        <ValidityScopeKind>::default()
    }
    fn valid_kmin(&self) -> u64 {
        0
    }
    fn valid_kmax(&self) -> u64 {
        0
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `Group<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 NullGroup<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullGroup<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullGroup<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullGroup<H> = NullGroup {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Group<H> for NullGroup<H> {
    type Operation = NullOperation<H>;
    fn generated_by(&self) -> &[Self::Operation] {
        &[]
    }
    fn order(&self) -> u64 {
        0
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `DihedralGroup<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 NullDihedralGroup<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullDihedralGroup<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullDihedralGroup<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullDihedralGroup<H> = NullDihedralGroup {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Group<H> for NullDihedralGroup<H> {
    type Operation = NullOperation<H>;
    fn generated_by(&self) -> &[Self::Operation] {
        &[]
    }
    fn order(&self) -> u64 {
        0
    }
}
impl<H: HostTypes> DihedralGroup<H> for NullDihedralGroup<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `WittLevelBinding<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 NullWittLevelBinding<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullWittLevelBinding<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullWittLevelBinding<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullWittLevelBinding<H> = NullWittLevelBinding {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> WittLevelBinding<H> for NullWittLevelBinding<H> {
    fn binding_level(&self) -> WittLevel {
        <WittLevel>::default()
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `QuantumThermodynamicDomain<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 NullQuantumThermodynamicDomain<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullQuantumThermodynamicDomain<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullQuantumThermodynamicDomain<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullQuantumThermodynamicDomain<H> = NullQuantumThermodynamicDomain {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> QuantumThermodynamicDomain<H> for NullQuantumThermodynamicDomain<H> {}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `ComposedOperation<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 NullComposedOperation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullComposedOperation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullComposedOperation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullComposedOperation<H> = NullComposedOperation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullComposedOperation<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> crate::user::morphism::Transform<H> for NullComposedOperation<H> {
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<H: HostTypes> crate::user::morphism::Composition<H> for NullComposedOperation<H> {
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<H: HostTypes> ComposedOperation<H> for NullComposedOperation<H> {
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `DispatchOperation<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 NullDispatchOperation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullDispatchOperation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullDispatchOperation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullDispatchOperation<H> = NullDispatchOperation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullDispatchOperation<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> crate::user::morphism::Transform<H> for NullDispatchOperation<H> {
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<H: HostTypes> crate::user::morphism::Composition<H> for NullDispatchOperation<H> {
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<H: HostTypes> ComposedOperation<H> for NullDispatchOperation<H> {
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<H: HostTypes> DispatchOperation<H> for NullDispatchOperation<H> {
    fn dispatch_source(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn dispatch_target(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `InferenceOperation<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 NullInferenceOperation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullInferenceOperation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullInferenceOperation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullInferenceOperation<H> = NullInferenceOperation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullInferenceOperation<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> crate::user::morphism::Transform<H> for NullInferenceOperation<H> {
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<H: HostTypes> crate::user::morphism::Composition<H> for NullInferenceOperation<H> {
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<H: HostTypes> ComposedOperation<H> for NullInferenceOperation<H> {
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<H: HostTypes> InferenceOperation<H> for NullInferenceOperation<H> {
    fn inference_source(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn inference_target(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn inference_pipeline(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `AccumulationOperation<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 NullAccumulationOperation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullAccumulationOperation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullAccumulationOperation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullAccumulationOperation<H> = NullAccumulationOperation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullAccumulationOperation<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> crate::user::morphism::Transform<H> for NullAccumulationOperation<H> {
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<H: HostTypes> crate::user::morphism::Composition<H> for NullAccumulationOperation<H> {
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<H: HostTypes> ComposedOperation<H> for NullAccumulationOperation<H> {
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<H: HostTypes> AccumulationOperation<H> for NullAccumulationOperation<H> {
    fn accumulation_base(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
    fn accumulation_binding(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `LeasePartitionOperation<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 NullLeasePartitionOperation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullLeasePartitionOperation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullLeasePartitionOperation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullLeasePartitionOperation<H> = NullLeasePartitionOperation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullLeasePartitionOperation<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> crate::user::morphism::Transform<H> for NullLeasePartitionOperation<H> {
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<H: HostTypes> crate::user::morphism::Composition<H> for NullLeasePartitionOperation<H> {
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<H: HostTypes> ComposedOperation<H> for NullLeasePartitionOperation<H> {
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<H: HostTypes> LeasePartitionOperation<H> for NullLeasePartitionOperation<H> {
    fn lease_source(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn lease_factor(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn lease_partition_count(&self) -> u64 {
        0
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `SessionCompositionOperation<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 NullSessionCompositionOperation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullSessionCompositionOperation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullSessionCompositionOperation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullSessionCompositionOperation<H> = NullSessionCompositionOperation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> Operation<H> for NullSessionCompositionOperation<H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<H: HostTypes> crate::user::morphism::Transform<H> for NullSessionCompositionOperation<H> {
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<H: HostTypes> crate::user::morphism::Composition<H> for NullSessionCompositionOperation<H> {
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<H: HostTypes> ComposedOperation<H> for NullSessionCompositionOperation<H> {
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<H: HostTypes> SessionCompositionOperation<H> for NullSessionCompositionOperation<H> {
    fn composition_left_session(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn composition_right_session(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
}

/// Phase 2 (orphan-closure) — resolver-absent default impl of `GroupPresentation<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 NullGroupPresentation<H: HostTypes> {
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Default for NullGroupPresentation<H> {
    fn default() -> Self {
        Self {
            _phantom: core::marker::PhantomData,
        }
    }
}
impl<H: HostTypes> NullGroupPresentation<H> {
    /// Absent-value sentinel. `&Self::ABSENT` gives every trait-typed accessor a `'static`-lifetime reference target.
    pub const ABSENT: NullGroupPresentation<H> = NullGroupPresentation {
        _phantom: core::marker::PhantomData,
    };
}
impl<H: HostTypes> GroupPresentation<H> for NullGroupPresentation<H> {}

/// Phase 8 (orphan-closure) — content-addressed handle for `Operation<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 OperationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for OperationHandle<H> {}
impl<H: HostTypes> Clone for OperationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for OperationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for OperationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for OperationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> OperationHandle<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 `Operation<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 OperationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: OperationHandle<H>) -> Option<OperationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `Operation<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 OperationRecord<H: HostTypes> {
    pub arity: u64,
    pub has_geometric_character: GeometricCharacter,
    pub inverse_handle: OperationHandle<H>,
    pub composed_of: &'static H::HostString,
    pub is_ring_op: bool,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `Operation<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 ResolvedOperation<'r, R: OperationResolver<H>, H: HostTypes> {
    handle: OperationHandle<H>,
    resolver: &'r R,
    record: Option<OperationRecord<H>>,
}
impl<'r, R: OperationResolver<H>, H: HostTypes> ResolvedOperation<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: OperationHandle<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) -> OperationHandle<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<&OperationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: OperationResolver<H>, H: HostTypes> Operation<H> for ResolvedOperation<'r, R, H> {
    fn arity(&self) -> u64 {
        match &self.record {
            Some(r) => r.arity,
            None => 0,
        }
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        match &self.record {
            Some(r) => r.has_geometric_character,
            None => <GeometricCharacter>::default(),
        }
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        match &self.record {
            Some(r) => r.is_ring_op,
            None => false,
        }
    }
}
impl<'r, R: OperationResolver<H>, H: HostTypes> ResolvedOperation<'r, R, H> {
    /// Promote the `inverse` 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_inverse<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(record.inverse_handle, r))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `UnaryOp<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 UnaryOpHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for UnaryOpHandle<H> {}
impl<H: HostTypes> Clone for UnaryOpHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for UnaryOpHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for UnaryOpHandle<H> {}
impl<H: HostTypes> core::hash::Hash for UnaryOpHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> UnaryOpHandle<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 `UnaryOp<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 UnaryOpResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: UnaryOpHandle<H>) -> Option<UnaryOpRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `UnaryOp<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 UnaryOpRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `UnaryOp<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 ResolvedUnaryOp<'r, R: UnaryOpResolver<H>, H: HostTypes> {
    handle: UnaryOpHandle<H>,
    resolver: &'r R,
    record: Option<UnaryOpRecord<H>>,
}
impl<'r, R: UnaryOpResolver<H>, H: HostTypes> ResolvedUnaryOp<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: UnaryOpHandle<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) -> UnaryOpHandle<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<&UnaryOpRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: UnaryOpResolver<H>, H: HostTypes> Operation<H> for ResolvedUnaryOp<'r, R, H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: UnaryOpResolver<H>, H: HostTypes> UnaryOp<H> for ResolvedUnaryOp<'r, R, H> {}

/// Phase 8 (orphan-closure) — content-addressed handle for `BinaryOp<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 BinaryOpHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for BinaryOpHandle<H> {}
impl<H: HostTypes> Clone for BinaryOpHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for BinaryOpHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for BinaryOpHandle<H> {}
impl<H: HostTypes> core::hash::Hash for BinaryOpHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> BinaryOpHandle<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 `BinaryOp<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 BinaryOpResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: BinaryOpHandle<H>) -> Option<BinaryOpRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `BinaryOp<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 BinaryOpRecord<H: HostTypes> {
    pub commutative: bool,
    pub associative: bool,
    pub identity: i64,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `BinaryOp<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 ResolvedBinaryOp<'r, R: BinaryOpResolver<H>, H: HostTypes> {
    handle: BinaryOpHandle<H>,
    resolver: &'r R,
    record: Option<BinaryOpRecord<H>>,
}
impl<'r, R: BinaryOpResolver<H>, H: HostTypes> ResolvedBinaryOp<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: BinaryOpHandle<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) -> BinaryOpHandle<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<&BinaryOpRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: BinaryOpResolver<H>, H: HostTypes> Operation<H> for ResolvedBinaryOp<'r, R, H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: BinaryOpResolver<H>, H: HostTypes> BinaryOp<H> for ResolvedBinaryOp<'r, R, H> {
    fn commutative(&self) -> bool {
        match &self.record {
            Some(r) => r.commutative,
            None => false,
        }
    }
    fn associative(&self) -> bool {
        match &self.record {
            Some(r) => r.associative,
            None => false,
        }
    }
    fn identity(&self) -> i64 {
        match &self.record {
            Some(r) => r.identity,
            None => 0,
        }
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `Involution<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 InvolutionHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for InvolutionHandle<H> {}
impl<H: HostTypes> Clone for InvolutionHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for InvolutionHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for InvolutionHandle<H> {}
impl<H: HostTypes> core::hash::Hash for InvolutionHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> InvolutionHandle<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 `Involution<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 InvolutionResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: InvolutionHandle<H>) -> Option<InvolutionRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `Involution<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 InvolutionRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `Involution<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 ResolvedInvolution<'r, R: InvolutionResolver<H>, H: HostTypes> {
    handle: InvolutionHandle<H>,
    resolver: &'r R,
    record: Option<InvolutionRecord<H>>,
}
impl<'r, R: InvolutionResolver<H>, H: HostTypes> ResolvedInvolution<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: InvolutionHandle<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) -> InvolutionHandle<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<&InvolutionRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: InvolutionResolver<H>, H: HostTypes> Operation<H> for ResolvedInvolution<'r, R, H> {
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: InvolutionResolver<H>, H: HostTypes> UnaryOp<H> for ResolvedInvolution<'r, R, H> {}
impl<'r, R: InvolutionResolver<H>, H: HostTypes> Involution<H> for ResolvedInvolution<'r, R, H> {}

/// Phase 8 (orphan-closure) — content-addressed handle for `Identity<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 IdentityHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for IdentityHandle<H> {}
impl<H: HostTypes> Clone for IdentityHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for IdentityHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for IdentityHandle<H> {}
impl<H: HostTypes> core::hash::Hash for IdentityHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> IdentityHandle<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 `Identity<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 IdentityResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: IdentityHandle<H>) -> Option<IdentityRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `Identity<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 IdentityRecord<H: HostTypes> {
    pub lhs_handle: crate::kernel::schema::TermExpressionHandle<H>,
    pub rhs_handle: crate::kernel::schema::TermExpressionHandle<H>,
    pub for_all_handle: crate::kernel::schema::ForAllDeclarationHandle<H>,
    pub universally_valid: bool,
    pub validity_kind: ValidityScopeKind,
    pub valid_kmin: u64,
    pub valid_kmax: u64,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `Identity<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 ResolvedIdentity<'r, R: IdentityResolver<H>, H: HostTypes> {
    handle: IdentityHandle<H>,
    resolver: &'r R,
    record: Option<IdentityRecord<H>>,
}
impl<'r, R: IdentityResolver<H>, H: HostTypes> ResolvedIdentity<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: IdentityHandle<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) -> IdentityHandle<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<&IdentityRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: IdentityResolver<H>, H: HostTypes> Identity<H> for ResolvedIdentity<'r, R, H> {
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn lhs(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
    fn rhs(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
    type ForAllDeclaration = crate::kernel::schema::NullForAllDeclaration<H>;
    fn for_all(&self) -> &Self::ForAllDeclaration {
        &<crate::kernel::schema::NullForAllDeclaration<H>>::ABSENT
    }
    fn verification_domain(&self) -> &[VerificationDomain] {
        &[]
    }
    type WittLevelBinding = NullWittLevelBinding<H>;
    fn verified_at_level(&self) -> &[Self::WittLevelBinding] {
        &[]
    }
    fn universally_valid(&self) -> bool {
        match &self.record {
            Some(r) => r.universally_valid,
            None => false,
        }
    }
    fn validity_kind(&self) -> ValidityScopeKind {
        match &self.record {
            Some(r) => r.validity_kind,
            None => <ValidityScopeKind>::default(),
        }
    }
    fn valid_kmin(&self) -> u64 {
        match &self.record {
            Some(r) => r.valid_kmin,
            None => 0,
        }
    }
    fn valid_kmax(&self) -> u64 {
        match &self.record {
            Some(r) => r.valid_kmax,
            None => 0,
        }
    }
}
impl<'r, R: IdentityResolver<H>, H: HostTypes> ResolvedIdentity<'r, R, H> {
    /// Promote the `lhs` 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_lhs<'r2, R2: crate::kernel::schema::TermExpressionResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::kernel::schema::ResolvedTermExpression<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::kernel::schema::ResolvedTermExpression::new(
            record.lhs_handle,
            r,
        ))
    }
    /// Promote the `rhs` 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_rhs<'r2, R2: crate::kernel::schema::TermExpressionResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::kernel::schema::ResolvedTermExpression<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::kernel::schema::ResolvedTermExpression::new(
            record.rhs_handle,
            r,
        ))
    }
    /// Promote the `for_all` 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_for_all<'r2, R2: crate::kernel::schema::ForAllDeclarationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::kernel::schema::ResolvedForAllDeclaration<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::kernel::schema::ResolvedForAllDeclaration::new(
            record.for_all_handle,
            r,
        ))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `Group<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 GroupHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for GroupHandle<H> {}
impl<H: HostTypes> Clone for GroupHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for GroupHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for GroupHandle<H> {}
impl<H: HostTypes> core::hash::Hash for GroupHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> GroupHandle<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 `Group<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 GroupResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: GroupHandle<H>) -> Option<GroupRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `Group<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 GroupRecord<H: HostTypes> {
    pub order: u64,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `Group<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 ResolvedGroup<'r, R: GroupResolver<H>, H: HostTypes> {
    handle: GroupHandle<H>,
    resolver: &'r R,
    record: Option<GroupRecord<H>>,
}
impl<'r, R: GroupResolver<H>, H: HostTypes> ResolvedGroup<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: GroupHandle<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) -> GroupHandle<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<&GroupRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: GroupResolver<H>, H: HostTypes> Group<H> for ResolvedGroup<'r, R, H> {
    type Operation = NullOperation<H>;
    fn generated_by(&self) -> &[Self::Operation] {
        &[]
    }
    fn order(&self) -> u64 {
        match &self.record {
            Some(r) => r.order,
            None => 0,
        }
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `DihedralGroup<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 DihedralGroupHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for DihedralGroupHandle<H> {}
impl<H: HostTypes> Clone for DihedralGroupHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for DihedralGroupHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for DihedralGroupHandle<H> {}
impl<H: HostTypes> core::hash::Hash for DihedralGroupHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> DihedralGroupHandle<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 `DihedralGroup<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 DihedralGroupResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: DihedralGroupHandle<H>) -> Option<DihedralGroupRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `DihedralGroup<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 DihedralGroupRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `DihedralGroup<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 ResolvedDihedralGroup<'r, R: DihedralGroupResolver<H>, H: HostTypes> {
    handle: DihedralGroupHandle<H>,
    resolver: &'r R,
    record: Option<DihedralGroupRecord<H>>,
}
impl<'r, R: DihedralGroupResolver<H>, H: HostTypes> ResolvedDihedralGroup<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: DihedralGroupHandle<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) -> DihedralGroupHandle<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<&DihedralGroupRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: DihedralGroupResolver<H>, H: HostTypes> Group<H> for ResolvedDihedralGroup<'r, R, H> {
    type Operation = NullOperation<H>;
    fn generated_by(&self) -> &[Self::Operation] {
        &[]
    }
    fn order(&self) -> u64 {
        0
    }
}
impl<'r, R: DihedralGroupResolver<H>, H: HostTypes> DihedralGroup<H>
    for ResolvedDihedralGroup<'r, R, H>
{
}

/// Phase 8 (orphan-closure) — content-addressed handle for `WittLevelBinding<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 WittLevelBindingHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for WittLevelBindingHandle<H> {}
impl<H: HostTypes> Clone for WittLevelBindingHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for WittLevelBindingHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for WittLevelBindingHandle<H> {}
impl<H: HostTypes> core::hash::Hash for WittLevelBindingHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> WittLevelBindingHandle<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 `WittLevelBinding<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 WittLevelBindingResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: WittLevelBindingHandle<H>) -> Option<WittLevelBindingRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `WittLevelBinding<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 WittLevelBindingRecord<H: HostTypes> {
    pub binding_level: WittLevel,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `WittLevelBinding<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 ResolvedWittLevelBinding<'r, R: WittLevelBindingResolver<H>, H: HostTypes> {
    handle: WittLevelBindingHandle<H>,
    resolver: &'r R,
    record: Option<WittLevelBindingRecord<H>>,
}
impl<'r, R: WittLevelBindingResolver<H>, H: HostTypes> ResolvedWittLevelBinding<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: WittLevelBindingHandle<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) -> WittLevelBindingHandle<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<&WittLevelBindingRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: WittLevelBindingResolver<H>, H: HostTypes> WittLevelBinding<H>
    for ResolvedWittLevelBinding<'r, R, H>
{
    fn binding_level(&self) -> WittLevel {
        match &self.record {
            Some(r) => r.binding_level,
            None => <WittLevel>::default(),
        }
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `QuantumThermodynamicDomain<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 QuantumThermodynamicDomainHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for QuantumThermodynamicDomainHandle<H> {}
impl<H: HostTypes> Clone for QuantumThermodynamicDomainHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for QuantumThermodynamicDomainHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for QuantumThermodynamicDomainHandle<H> {}
impl<H: HostTypes> core::hash::Hash for QuantumThermodynamicDomainHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> QuantumThermodynamicDomainHandle<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 `QuantumThermodynamicDomain<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 QuantumThermodynamicDomainResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(
        &self,
        handle: QuantumThermodynamicDomainHandle<H>,
    ) -> Option<QuantumThermodynamicDomainRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `QuantumThermodynamicDomain<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 QuantumThermodynamicDomainRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `QuantumThermodynamicDomain<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 ResolvedQuantumThermodynamicDomain<
    'r,
    R: QuantumThermodynamicDomainResolver<H>,
    H: HostTypes,
> {
    handle: QuantumThermodynamicDomainHandle<H>,
    resolver: &'r R,
    record: Option<QuantumThermodynamicDomainRecord<H>>,
}
impl<'r, R: QuantumThermodynamicDomainResolver<H>, H: HostTypes>
    ResolvedQuantumThermodynamicDomain<'r, R, H>
{
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: QuantumThermodynamicDomainHandle<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) -> QuantumThermodynamicDomainHandle<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<&QuantumThermodynamicDomainRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: QuantumThermodynamicDomainResolver<H>, H: HostTypes> QuantumThermodynamicDomain<H>
    for ResolvedQuantumThermodynamicDomain<'r, R, H>
{
}

/// Phase 8 (orphan-closure) — content-addressed handle for `ComposedOperation<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 ComposedOperationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for ComposedOperationHandle<H> {}
impl<H: HostTypes> Clone for ComposedOperationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for ComposedOperationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for ComposedOperationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for ComposedOperationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> ComposedOperationHandle<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 `ComposedOperation<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 ComposedOperationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: ComposedOperationHandle<H>) -> Option<ComposedOperationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `ComposedOperation<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 ComposedOperationRecord<H: HostTypes> {
    pub operator_domain_type_handle: crate::user::type_::TypeDefinitionHandle<H>,
    pub operator_range_type_handle: crate::user::type_::TypeDefinitionHandle<H>,
    pub operator_complexity: &'static H::HostString,
    pub operator_idempotent: bool,
    pub composed_operator_count: u64,
    pub is_involutory: bool,
    pub convergence_guarantee_handle: crate::kernel::schema::TermExpressionHandle<H>,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `ComposedOperation<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 ResolvedComposedOperation<'r, R: ComposedOperationResolver<H>, H: HostTypes> {
    handle: ComposedOperationHandle<H>,
    resolver: &'r R,
    record: Option<ComposedOperationRecord<H>>,
}
impl<'r, R: ComposedOperationResolver<H>, H: HostTypes> ResolvedComposedOperation<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: ComposedOperationHandle<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) -> ComposedOperationHandle<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<&ComposedOperationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: ComposedOperationResolver<H>, H: HostTypes> Operation<H>
    for ResolvedComposedOperation<'r, R, H>
{
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: ComposedOperationResolver<H>, H: HostTypes> crate::user::morphism::Transform<H>
    for ResolvedComposedOperation<'r, R, H>
{
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<'r, R: ComposedOperationResolver<H>, H: HostTypes> crate::user::morphism::Composition<H>
    for ResolvedComposedOperation<'r, R, H>
{
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<'r, R: ComposedOperationResolver<H>, H: HostTypes> ComposedOperation<H>
    for ResolvedComposedOperation<'r, R, H>
{
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        match &self.record {
            Some(r) => r.operator_complexity,
            None => H::EMPTY_HOST_STRING,
        }
    }
    fn operator_idempotent(&self) -> bool {
        match &self.record {
            Some(r) => r.operator_idempotent,
            None => false,
        }
    }
    fn composed_operator_count(&self) -> u64 {
        match &self.record {
            Some(r) => r.composed_operator_count,
            None => 0,
        }
    }
    fn is_involutory(&self) -> bool {
        match &self.record {
            Some(r) => r.is_involutory,
            None => false,
        }
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<'r, R: ComposedOperationResolver<H>, H: HostTypes> ResolvedComposedOperation<'r, R, H> {
    /// Promote the `operator_domain_type` 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_operator_domain_type<'r2, R2: crate::user::type_::TypeDefinitionResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::user::type_::ResolvedTypeDefinition<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::user::type_::ResolvedTypeDefinition::new(
            record.operator_domain_type_handle,
            r,
        ))
    }
    /// Promote the `operator_range_type` 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_operator_range_type<'r2, R2: crate::user::type_::TypeDefinitionResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::user::type_::ResolvedTypeDefinition<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::user::type_::ResolvedTypeDefinition::new(
            record.operator_range_type_handle,
            r,
        ))
    }
    /// Promote the `convergence_guarantee` 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_convergence_guarantee<
        'r2,
        R2: crate::kernel::schema::TermExpressionResolver<H>,
    >(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::kernel::schema::ResolvedTermExpression<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::kernel::schema::ResolvedTermExpression::new(
            record.convergence_guarantee_handle,
            r,
        ))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `DispatchOperation<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 DispatchOperationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for DispatchOperationHandle<H> {}
impl<H: HostTypes> Clone for DispatchOperationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for DispatchOperationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for DispatchOperationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for DispatchOperationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> DispatchOperationHandle<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 `DispatchOperation<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 DispatchOperationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: DispatchOperationHandle<H>) -> Option<DispatchOperationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `DispatchOperation<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 DispatchOperationRecord<H: HostTypes> {
    pub dispatch_source_handle: OperationHandle<H>,
    pub dispatch_target_handle: OperationHandle<H>,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `DispatchOperation<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 ResolvedDispatchOperation<'r, R: DispatchOperationResolver<H>, H: HostTypes> {
    handle: DispatchOperationHandle<H>,
    resolver: &'r R,
    record: Option<DispatchOperationRecord<H>>,
}
impl<'r, R: DispatchOperationResolver<H>, H: HostTypes> ResolvedDispatchOperation<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: DispatchOperationHandle<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) -> DispatchOperationHandle<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<&DispatchOperationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: DispatchOperationResolver<H>, H: HostTypes> Operation<H>
    for ResolvedDispatchOperation<'r, R, H>
{
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: DispatchOperationResolver<H>, H: HostTypes> crate::user::morphism::Transform<H>
    for ResolvedDispatchOperation<'r, R, H>
{
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<'r, R: DispatchOperationResolver<H>, H: HostTypes> crate::user::morphism::Composition<H>
    for ResolvedDispatchOperation<'r, R, H>
{
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<'r, R: DispatchOperationResolver<H>, H: HostTypes> ComposedOperation<H>
    for ResolvedDispatchOperation<'r, R, H>
{
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<'r, R: DispatchOperationResolver<H>, H: HostTypes> DispatchOperation<H>
    for ResolvedDispatchOperation<'r, R, H>
{
    fn dispatch_source(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn dispatch_target(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
}
impl<'r, R: DispatchOperationResolver<H>, H: HostTypes> ResolvedDispatchOperation<'r, R, H> {
    /// Promote the `dispatch_source` 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_dispatch_source<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(record.dispatch_source_handle, r))
    }
    /// Promote the `dispatch_target` 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_dispatch_target<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(record.dispatch_target_handle, r))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `InferenceOperation<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 InferenceOperationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for InferenceOperationHandle<H> {}
impl<H: HostTypes> Clone for InferenceOperationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for InferenceOperationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for InferenceOperationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for InferenceOperationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> InferenceOperationHandle<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 `InferenceOperation<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 InferenceOperationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: InferenceOperationHandle<H>) -> Option<InferenceOperationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `InferenceOperation<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 InferenceOperationRecord<H: HostTypes> {
    pub inference_source_handle: OperationHandle<H>,
    pub inference_target_handle: OperationHandle<H>,
    pub inference_pipeline_handle: OperationHandle<H>,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `InferenceOperation<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 ResolvedInferenceOperation<'r, R: InferenceOperationResolver<H>, H: HostTypes> {
    handle: InferenceOperationHandle<H>,
    resolver: &'r R,
    record: Option<InferenceOperationRecord<H>>,
}
impl<'r, R: InferenceOperationResolver<H>, H: HostTypes> ResolvedInferenceOperation<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: InferenceOperationHandle<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) -> InferenceOperationHandle<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<&InferenceOperationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: InferenceOperationResolver<H>, H: HostTypes> Operation<H>
    for ResolvedInferenceOperation<'r, R, H>
{
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: InferenceOperationResolver<H>, H: HostTypes> crate::user::morphism::Transform<H>
    for ResolvedInferenceOperation<'r, R, H>
{
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<'r, R: InferenceOperationResolver<H>, H: HostTypes> crate::user::morphism::Composition<H>
    for ResolvedInferenceOperation<'r, R, H>
{
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<'r, R: InferenceOperationResolver<H>, H: HostTypes> ComposedOperation<H>
    for ResolvedInferenceOperation<'r, R, H>
{
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<'r, R: InferenceOperationResolver<H>, H: HostTypes> InferenceOperation<H>
    for ResolvedInferenceOperation<'r, R, H>
{
    fn inference_source(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn inference_target(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn inference_pipeline(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
}
impl<'r, R: InferenceOperationResolver<H>, H: HostTypes> ResolvedInferenceOperation<'r, R, H> {
    /// Promote the `inference_source` 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_inference_source<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(record.inference_source_handle, r))
    }
    /// Promote the `inference_target` 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_inference_target<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(record.inference_target_handle, r))
    }
    /// Promote the `inference_pipeline` 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_inference_pipeline<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(record.inference_pipeline_handle, r))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `AccumulationOperation<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 AccumulationOperationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for AccumulationOperationHandle<H> {}
impl<H: HostTypes> Clone for AccumulationOperationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for AccumulationOperationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for AccumulationOperationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for AccumulationOperationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> AccumulationOperationHandle<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 `AccumulationOperation<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 AccumulationOperationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(
        &self,
        handle: AccumulationOperationHandle<H>,
    ) -> Option<AccumulationOperationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `AccumulationOperation<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 AccumulationOperationRecord<H: HostTypes> {
    pub accumulation_base_handle: crate::kernel::schema::TermExpressionHandle<H>,
    pub accumulation_binding_handle: crate::kernel::schema::TermExpressionHandle<H>,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `AccumulationOperation<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 ResolvedAccumulationOperation<'r, R: AccumulationOperationResolver<H>, H: HostTypes> {
    handle: AccumulationOperationHandle<H>,
    resolver: &'r R,
    record: Option<AccumulationOperationRecord<H>>,
}
impl<'r, R: AccumulationOperationResolver<H>, H: HostTypes>
    ResolvedAccumulationOperation<'r, R, H>
{
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: AccumulationOperationHandle<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) -> AccumulationOperationHandle<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<&AccumulationOperationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: AccumulationOperationResolver<H>, H: HostTypes> Operation<H>
    for ResolvedAccumulationOperation<'r, R, H>
{
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: AccumulationOperationResolver<H>, H: HostTypes> crate::user::morphism::Transform<H>
    for ResolvedAccumulationOperation<'r, R, H>
{
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<'r, R: AccumulationOperationResolver<H>, H: HostTypes> crate::user::morphism::Composition<H>
    for ResolvedAccumulationOperation<'r, R, H>
{
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<'r, R: AccumulationOperationResolver<H>, H: HostTypes> ComposedOperation<H>
    for ResolvedAccumulationOperation<'r, R, H>
{
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<'r, R: AccumulationOperationResolver<H>, H: HostTypes> AccumulationOperation<H>
    for ResolvedAccumulationOperation<'r, R, H>
{
    fn accumulation_base(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
    fn accumulation_binding(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<'r, R: AccumulationOperationResolver<H>, H: HostTypes>
    ResolvedAccumulationOperation<'r, R, H>
{
    /// Promote the `accumulation_base` 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_accumulation_base<'r2, R2: crate::kernel::schema::TermExpressionResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::kernel::schema::ResolvedTermExpression<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::kernel::schema::ResolvedTermExpression::new(
            record.accumulation_base_handle,
            r,
        ))
    }
    /// Promote the `accumulation_binding` 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_accumulation_binding<
        'r2,
        R2: crate::kernel::schema::TermExpressionResolver<H>,
    >(
        &self,
        r: &'r2 R2,
    ) -> Option<crate::kernel::schema::ResolvedTermExpression<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(crate::kernel::schema::ResolvedTermExpression::new(
            record.accumulation_binding_handle,
            r,
        ))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `LeasePartitionOperation<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 LeasePartitionOperationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for LeasePartitionOperationHandle<H> {}
impl<H: HostTypes> Clone for LeasePartitionOperationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for LeasePartitionOperationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for LeasePartitionOperationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for LeasePartitionOperationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> LeasePartitionOperationHandle<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 `LeasePartitionOperation<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 LeasePartitionOperationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(
        &self,
        handle: LeasePartitionOperationHandle<H>,
    ) -> Option<LeasePartitionOperationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `LeasePartitionOperation<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 LeasePartitionOperationRecord<H: HostTypes> {
    pub lease_source_handle: OperationHandle<H>,
    pub lease_factor_handle: OperationHandle<H>,
    pub lease_partition_count: u64,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `LeasePartitionOperation<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 ResolvedLeasePartitionOperation<'r, R: LeasePartitionOperationResolver<H>, H: HostTypes>
{
    handle: LeasePartitionOperationHandle<H>,
    resolver: &'r R,
    record: Option<LeasePartitionOperationRecord<H>>,
}
impl<'r, R: LeasePartitionOperationResolver<H>, H: HostTypes>
    ResolvedLeasePartitionOperation<'r, R, H>
{
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: LeasePartitionOperationHandle<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) -> LeasePartitionOperationHandle<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<&LeasePartitionOperationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: LeasePartitionOperationResolver<H>, H: HostTypes> Operation<H>
    for ResolvedLeasePartitionOperation<'r, R, H>
{
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: LeasePartitionOperationResolver<H>, H: HostTypes> crate::user::morphism::Transform<H>
    for ResolvedLeasePartitionOperation<'r, R, H>
{
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<'r, R: LeasePartitionOperationResolver<H>, H: HostTypes> crate::user::morphism::Composition<H>
    for ResolvedLeasePartitionOperation<'r, R, H>
{
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<'r, R: LeasePartitionOperationResolver<H>, H: HostTypes> ComposedOperation<H>
    for ResolvedLeasePartitionOperation<'r, R, H>
{
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<'r, R: LeasePartitionOperationResolver<H>, H: HostTypes> LeasePartitionOperation<H>
    for ResolvedLeasePartitionOperation<'r, R, H>
{
    fn lease_source(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn lease_factor(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn lease_partition_count(&self) -> u64 {
        match &self.record {
            Some(r) => r.lease_partition_count,
            None => 0,
        }
    }
}
impl<'r, R: LeasePartitionOperationResolver<H>, H: HostTypes>
    ResolvedLeasePartitionOperation<'r, R, H>
{
    /// Promote the `lease_source` 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_lease_source<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(record.lease_source_handle, r))
    }
    /// Promote the `lease_factor` 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_lease_factor<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(record.lease_factor_handle, r))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `SessionCompositionOperation<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 SessionCompositionOperationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for SessionCompositionOperationHandle<H> {}
impl<H: HostTypes> Clone for SessionCompositionOperationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for SessionCompositionOperationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for SessionCompositionOperationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for SessionCompositionOperationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> SessionCompositionOperationHandle<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 `SessionCompositionOperation<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 SessionCompositionOperationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(
        &self,
        handle: SessionCompositionOperationHandle<H>,
    ) -> Option<SessionCompositionOperationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `SessionCompositionOperation<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 SessionCompositionOperationRecord<H: HostTypes> {
    pub composition_left_session_handle: OperationHandle<H>,
    pub composition_right_session_handle: OperationHandle<H>,
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `SessionCompositionOperation<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 ResolvedSessionCompositionOperation<
    'r,
    R: SessionCompositionOperationResolver<H>,
    H: HostTypes,
> {
    handle: SessionCompositionOperationHandle<H>,
    resolver: &'r R,
    record: Option<SessionCompositionOperationRecord<H>>,
}
impl<'r, R: SessionCompositionOperationResolver<H>, H: HostTypes>
    ResolvedSessionCompositionOperation<'r, R, H>
{
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: SessionCompositionOperationHandle<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) -> SessionCompositionOperationHandle<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<&SessionCompositionOperationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: SessionCompositionOperationResolver<H>, H: HostTypes> Operation<H>
    for ResolvedSessionCompositionOperation<'r, R, H>
{
    fn arity(&self) -> u64 {
        0
    }
    fn has_geometric_character(&self) -> GeometricCharacter {
        <GeometricCharacter>::default()
    }
    type OperationTarget = NullOperation<H>;
    fn inverse(&self) -> &Self::OperationTarget {
        &<NullOperation<H>>::ABSENT
    }
    fn composed_of(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn is_ring_op(&self) -> bool {
        false
    }
}
impl<'r, R: SessionCompositionOperationResolver<H>, H: HostTypes>
    crate::user::morphism::Transform<H> for ResolvedSessionCompositionOperation<'r, R, H>
{
    fn source(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn target(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn preserves_count(&self) -> usize {
        0
    }
    fn preserves_at(&self, _index: usize) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type ComputationTrace = crate::bridge::trace::NullComputationTrace<H>;
    fn trace(&self) -> &Self::ComputationTrace {
        &<crate::bridge::trace::NullComputationTrace<H>>::ABSENT
    }
    type TransformTarget = crate::user::morphism::NullTransform<H>;
    fn composes_with(&self) -> &[Self::TransformTarget] {
        &[]
    }
    type Identity = NullIdentity<H>;
    fn preserved_invariant(&self) -> &Self::Identity {
        &<NullIdentity<H>>::ABSENT
    }
    fn input_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn output_class(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    type Witness = crate::user::morphism::NullWitness<H>;
    fn has_witness(&self) -> &[Self::Witness] {
        &[]
    }
}
impl<'r, R: SessionCompositionOperationResolver<H>, H: HostTypes>
    crate::user::morphism::Composition<H> for ResolvedSessionCompositionOperation<'r, R, H>
{
    type Transform = crate::user::morphism::NullTransform<H>;
    fn composition_result(&self) -> &Self::Transform {
        &<crate::user::morphism::NullTransform<H>>::ABSENT
    }
    fn composition_components(&self) -> &[Self::Transform] {
        &[]
    }
}
impl<'r, R: SessionCompositionOperationResolver<H>, H: HostTypes> ComposedOperation<H>
    for ResolvedSessionCompositionOperation<'r, R, H>
{
    type Operation = NullOperation<H>;
    fn composed_of_ops(&self) -> &[Self::Operation] {
        &[]
    }
    type TypeDefinition = crate::user::type_::NullTypeDefinition<H>;
    fn operator_domain_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_range_type(&self) -> &Self::TypeDefinition {
        &<crate::user::type_::NullTypeDefinition<H>>::ABSENT
    }
    fn operator_complexity(&self) -> &H::HostString {
        H::EMPTY_HOST_STRING
    }
    fn operator_idempotent(&self) -> bool {
        false
    }
    fn composed_operator_count(&self) -> u64 {
        0
    }
    fn is_involutory(&self) -> bool {
        false
    }
    type TermExpression = crate::kernel::schema::NullTermExpression<H>;
    fn convergence_guarantee(&self) -> &Self::TermExpression {
        &<crate::kernel::schema::NullTermExpression<H>>::ABSENT
    }
}
impl<'r, R: SessionCompositionOperationResolver<H>, H: HostTypes> SessionCompositionOperation<H>
    for ResolvedSessionCompositionOperation<'r, R, H>
{
    fn composition_left_session(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
    fn composition_right_session(&self) -> &Self::Operation {
        &<NullOperation<H>>::ABSENT
    }
}
impl<'r, R: SessionCompositionOperationResolver<H>, H: HostTypes>
    ResolvedSessionCompositionOperation<'r, R, H>
{
    /// Promote the `composition_left_session` 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_composition_left_session<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(
            record.composition_left_session_handle,
            r,
        ))
    }
    /// Promote the `composition_right_session` 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_composition_right_session<'r2, R2: OperationResolver<H>>(
        &self,
        r: &'r2 R2,
    ) -> Option<ResolvedOperation<'r2, R2, H>> {
        let record = self.record.as_ref()?;
        Some(ResolvedOperation::new(
            record.composition_right_session_handle,
            r,
        ))
    }
}

/// Phase 8 (orphan-closure) — content-addressed handle for `GroupPresentation<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 GroupPresentationHandle<H: HostTypes> {
    /// Content fingerprint identifying the resolved record.
    pub fingerprint: crate::enforcement::ContentFingerprint,
    _phantom: core::marker::PhantomData<H>,
}
impl<H: HostTypes> Copy for GroupPresentationHandle<H> {}
impl<H: HostTypes> Clone for GroupPresentationHandle<H> {
    #[inline]
    fn clone(&self) -> Self {
        *self
    }
}
impl<H: HostTypes> PartialEq for GroupPresentationHandle<H> {
    #[inline]
    fn eq(&self, other: &Self) -> bool {
        self.fingerprint == other.fingerprint
    }
}
impl<H: HostTypes> Eq for GroupPresentationHandle<H> {}
impl<H: HostTypes> core::hash::Hash for GroupPresentationHandle<H> {
    #[inline]
    fn hash<S: core::hash::Hasher>(&self, state: &mut S) {
        self.fingerprint.hash(state);
    }
}
impl<H: HostTypes> GroupPresentationHandle<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 `GroupPresentation<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 GroupPresentationResolver<H: HostTypes> {
    /// Resolve a handle into its record. Returns `None` when the
    /// handle does not correspond to known content.
    fn resolve(&self, handle: GroupPresentationHandle<H>) -> Option<GroupPresentationRecord<H>>;
}

/// Phase 8 (orphan-closure) — typed record for `GroupPresentation<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 GroupPresentationRecord<H: HostTypes> {
    #[doc(hidden)]
    pub _phantom: core::marker::PhantomData<H>,
}

/// Phase 8 (orphan-closure) — content-addressed wrapper for `GroupPresentation<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 ResolvedGroupPresentation<'r, R: GroupPresentationResolver<H>, H: HostTypes> {
    handle: GroupPresentationHandle<H>,
    resolver: &'r R,
    record: Option<GroupPresentationRecord<H>>,
}
impl<'r, R: GroupPresentationResolver<H>, H: HostTypes> ResolvedGroupPresentation<'r, R, H> {
    /// Construct the wrapper, eagerly resolving the handle.
    #[inline]
    pub fn new(handle: GroupPresentationHandle<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) -> GroupPresentationHandle<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<&GroupPresentationRecord<H>> {
        self.record.as_ref()
    }
}
impl<'r, R: GroupPresentationResolver<H>, H: HostTypes> GroupPresentation<H>
    for ResolvedGroupPresentation<'r, R, H>
{
}

/// Established by exhaustive traversal of R_n. Valid for all identities where the ring is finite.
pub mod enumerative {
    /// `enumVariant` -> `Enumerative`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/Enumerative";
}

/// Established by equational reasoning from ring or group axioms. Covers derivations via associativity, commutativity, inverse laws, and group presentations.
pub mod algebraic {
    /// `enumVariant` -> `Algebraic`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/Algebraic";
}

/// Established by isometry, symmetry, or GeometricCharacter arguments. Covers dihedral actions, fixed-point analysis, automorphism groups, and affine embeddings.
pub mod geometric {
    /// `enumVariant` -> `Geometric`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/Geometric";
}

/// Established via discrete differential calculus or metric analysis. Covers ring/Hamming derivatives (DC_), metric divergence (AM_), and adiabatic scheduling (AR_).
pub mod analytical {
    /// `enumVariant` -> `Analytical`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/Analytical";
}

/// Established via entropy, Landauer bounds, or Boltzmann distributions. Covers site entropy (TH_), reversible computation (RC_), and phase transitions.
pub mod thermodynamic {
    /// `enumVariant` -> `Thermodynamic`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Established via simplicial homology, cohomology, or constraint nerve analysis. Covers homological algebra (HA_) and the ψ-pipeline base chain ψ_1..ψ_6 (constraint nerve construction, chain functor, homology, Betti extraction, dualization, cohomology).
pub mod topological {
    /// `enumVariant` -> `Topological`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/Topological";
}

/// Established by the inter-algebra map structure of the resolution pipeline. Covers φ-maps (phi_1–phi_6) and the ψ-pipeline tower ψ_7..ψ_9 (Postnikov truncation, homotopy group extraction, k-invariant computation). The earlier ψ_1..ψ_6 chain (constraint nerve → simplicial homology) is established under op:Topological.
pub mod pipeline {
    /// `enumVariant` -> `Pipeline`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/Pipeline";
}

/// Established by the composition of Analytical and Topological reasoning. The only domain requiring multiple op:verificationDomain assertions. Covers the UOR Index Theorem (IT_7a–IT_7d).
pub mod index_theoretic {
    /// `enumVariant` -> `IndexTheoretic`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Established by superposition analysis of site states. Covers identities involving superposed (non-classical) site assignments where sites carry complex amplitudes.
pub mod superposition_domain {
    /// `enumVariant` -> `SuperpositionDomain`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/SuperpositionDomain";
}

/// Established by the intersection of quantum superposition analysis and classical thermodynamic reasoning. Covers identities relating von Neumann entropy of superposed states to Landauer costs of projective collapse (QM_).
pub mod quantum_thermodynamic {
    /// `enumVariant` -> `QuantumThermodynamic`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/QuantumThermodynamic";
}

/// Established by number-theoretic valuation arguments including p-adic absolute values, the Ostrowski product formula, and the arithmetic of global fields. Covers identities grounded in the product formula |x|_p · |x|_∞ = 1 and the Witt–Ostrowski derivation chain.
pub mod arithmetic_valuation {
    /// `enumVariant` -> `ArithmeticValuation`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/ArithmeticValuation";
}

/// Verification domain for composed operation identities — algebraic properties of operator compositions including dispatch, inference, accumulation, lease, and session composition operations.
pub mod composed_algebraic {
    /// `enumVariant` -> `ComposedAlgebraic`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Holds for all k in N. No minimum k constraint.
pub mod universal {
    /// `enumVariant` -> `Universal`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/Universal";
}

/// Holds for all k >= k_min, where k_min is given by validKMin.
pub mod parametric_lower {
    /// `enumVariant` -> `ParametricLower`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/ParametricLower";
}

/// Holds for k_min <= k <= k_max. Both validKMin and validKMax required.
pub mod parametric_range {
    /// `enumVariant` -> `ParametricRange`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/ParametricRange";
}

/// Holds only at exactly one level, given by a WittLevelBinding.
pub mod level_specific {
    /// `enumVariant` -> `LevelSpecific`
    pub const ENUM_VARIANT: &str = "https://uor.foundation/op/LevelSpecific";
}

/// Reflection through the origin of the additive ring: neg(x) = -x mod 2^n. One of the two generators of D_{2^n}.
pub mod ring_reflection {}

/// Reflection through the centre of the hypercube: bnot(x) = (2^n-1) ⊕ x. The second generator of D_{2^n}.
pub mod hypercube_reflection {}

/// Rotation by one step: succ(x) = (x+1) mod 2^n. The composition of the two reflections.
pub mod rotation {}

/// Rotation by one step in the reverse direction: pred(x) = (x-1) mod 2^n.
pub mod rotation_inverse {}

/// Translation along the ring axis: add(x,y), sub(x,y). Preserves Hamming distance locally.
pub mod translation {}

/// Scaling along the ring axis: mul(x,y) = (x×y) mod 2^n.
pub mod scaling {}

/// Translation along the hypercube axis: xor(x,y) = x ⊕ y. Preserves ring distance locally.
pub mod hypercube_translation {}

/// Projection onto a hypercube face: and(x,y) = x ∧ y. Idempotent; collapses dimensions.
pub mod hypercube_projection {}

/// Join on the hypercube lattice: or(x,y) = x ∨ y. Idempotent; dual to projection.
pub mod hypercube_join {}

/// Euclidean quotient along the ring axis: div(a,b) — the structural dual of Scaling. Geometric character of `op:div` per ADR-053.
pub mod quotient {}

/// Euclidean remainder along the ring axis: mod(a,b). Complement of Quotient — together they realize the divmod fold-rule. Geometric character of `op:mod` per ADR-053.
pub mod remainder {}

/// Iterated multiplicative scaling along the ring axis: pow(base, exp) = base^exp mod 2^n. Extends the multiplicative Scaling axis via square-and-multiply iteration. Geometric character of `op:pow` per ADR-053.
pub mod iterated_scaling {}

/// Geometric character of dispatch: constraint-guided selection over the resolver registry lattice.
pub mod constraint_selection {}

/// Geometric character of inference: traversal through the φ-pipeline resolution graph P ∘ Π ∘ G.
pub mod resolution_traversal {}

/// Geometric character of accumulation: progressive pinning of site states in the context lattice.
pub mod site_binding {}

/// Geometric character of lease partition: splitting a shared context into disjoint site-set leases.
pub mod site_partition {}

/// Geometric character of session composition: merging disjoint lease sessions into a unified resolution context.
pub mod session_merge {}

/// δ(q, R) = R(q): dispatches a query to the matching resolver in the registry. Non-commutative, non-associative.
pub mod dispatch {
    /// `arity`
    pub const ARITY: i64 = 2;
    /// `associative`
    pub const ASSOCIATIVE: bool = false;
    /// `commutative`
    pub const COMMUTATIVE: bool = false;
    /// `hasGeometricCharacter` -> `ConstraintSelection`
    pub const HAS_GEOMETRIC_CHARACTER: &str = "https://uor.foundation/op/ConstraintSelection";
    /// `operatorSignature`
    pub const OPERATOR_SIGNATURE: &str = "Query × ResolverRegistry → Resolver";
}

/// ι(s, C) = P(Π(G(s, C))): the φ-pipeline composed into a single inference step. Non-commutative, non-associative.
pub mod infer {
    /// `arity`
    pub const ARITY: i64 = 2;
    /// `associative`
    pub const ASSOCIATIVE: bool = false;
    /// `commutative`
    pub const COMMUTATIVE: bool = false;
    /// `hasGeometricCharacter` -> `ResolutionTraversal`
    pub const HAS_GEOMETRIC_CHARACTER: &str = "https://uor.foundation/op/ResolutionTraversal";
    /// `operatorSignature`
    pub const OPERATOR_SIGNATURE: &str = "Symbol × Context → ResolvedType";
}

/// α(b, C) = C': accumulates a binding into a resolution context, pinning a site. Non-commutative, associative at convergence (SR_10).
pub mod accumulate {
    /// `arity`
    pub const ARITY: i64 = 2;
    /// `associative`
    pub const ASSOCIATIVE: bool = true;
    /// `commutative`
    pub const COMMUTATIVE: bool = false;
    /// `hasGeometricCharacter` -> `SiteBinding`
    pub const HAS_GEOMETRIC_CHARACTER: &str = "https://uor.foundation/op/SiteBinding";
    /// `operatorSignature`
    pub const OPERATOR_SIGNATURE: &str = "Binding × Context → Context";
}

/// λ(S, k) = (L₁, …, Lₖ): partitions a shared context into k disjoint leases. Non-commutative, non-associative.
pub mod partition_op {
    /// `arity`
    pub const ARITY: i64 = 2;
    /// `associative`
    pub const ASSOCIATIVE: bool = false;
    /// `commutative`
    pub const COMMUTATIVE: bool = false;
    /// `hasGeometricCharacter` -> `SitePartition`
    pub const HAS_GEOMETRIC_CHARACTER: &str = "https://uor.foundation/op/SitePartition";
    /// `operatorSignature`
    pub const OPERATOR_SIGNATURE: &str = "SharedContext × ℕ → ContextLease^k";
}

/// κ(S₁, S₂) = S₁ ∪ S₂: composes two sessions with disjoint leases into one. Commutative, associative (SR_8).
pub mod compose_op {
    /// `arity`
    pub const ARITY: i64 = 2;
    /// `associative`
    pub const ASSOCIATIVE: bool = true;
    /// `commutative`
    pub const COMMUTATIVE: bool = true;
    /// `hasGeometricCharacter` -> `SessionMerge`
    pub const HAS_GEOMETRIC_CHARACTER: &str = "https://uor.foundation/op/SessionMerge";
    /// `operatorSignature`
    pub const OPERATOR_SIGNATURE: &str = "Session × Session → Session";
}

/// The foundational theorem of the UOR kernel: neg(bnot(x)) = succ(x) for all x in R_n. This identity links the two involutions (neg and bnot) to the successor operation, making succ derivable from neg and bnot.
pub mod critical_identity {
    /// `forAll` -> `term_criticalIdentity_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_criticalIdentity_forAll";
    /// `lhs` -> `term_criticalIdentity_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_criticalIdentity_lhs";
    /// `rhs` -> `term_criticalIdentity_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_criticalIdentity_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Addressing bijection: addresses(glyph(d)) = d. Round-trip from datum through glyph and back is identity.
pub mod ad_1 {
    /// `forAll` -> `term_AD_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AD_1_forAll";
    /// `lhs` -> `term_AD_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AD_1_lhs";
    /// `rhs` -> `term_AD_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AD_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Embedding coherence: glyph(ι(addresses(a))) = ι_addr(a). The addressing diagram commutes through embeddings.
pub mod ad_2 {
    /// `forAll` -> `term_AD_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AD_2_forAll";
    /// `lhs` -> `term_AD_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AD_2_lhs";
    /// `rhs` -> `term_AD_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AD_2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Additive associativity: add(x, add(y, z)) = add(add(x, y), z).
pub mod r_a1 {
    /// `forAll` -> `term_R_A1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_A1_forAll";
    /// `lhs` -> `term_R_A1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_A1_lhs";
    /// `rhs` -> `term_R_A1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_A1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Additive identity: add(x, 0) = x.
pub mod r_a2 {
    /// `forAll` -> `term_R_A2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_A2_forAll";
    /// `lhs` -> `term_R_A2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_A2_lhs";
    /// `rhs` -> `term_R_A2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_A2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Additive inverse: add(x, neg(x)) = 0.
pub mod r_a3 {
    /// `forAll` -> `term_R_A3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_A3_forAll";
    /// `lhs` -> `term_R_A3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_A3_lhs";
    /// `rhs` -> `term_R_A3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_A3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Additive commutativity: add(x, y) = add(y, x).
pub mod r_a4 {
    /// `forAll` -> `term_R_A4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_A4_forAll";
    /// `lhs` -> `term_R_A4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_A4_lhs";
    /// `rhs` -> `term_R_A4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_A4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Subtraction definition: sub(x, y) = add(x, neg(y)).
pub mod r_a5 {
    /// `forAll` -> `term_R_A5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_A5_forAll";
    /// `lhs` -> `term_R_A5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_A5_lhs";
    /// `rhs` -> `term_R_A5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_A5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Negation involution: neg(neg(x)) = x.
pub mod r_a6 {
    /// `forAll` -> `term_R_A6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_A6_forAll";
    /// `lhs` -> `term_R_A6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_A6_lhs";
    /// `rhs` -> `term_R_A6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_A6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Multiplicative associativity: mul(x, mul(y, z)) = mul(mul(x, y), z).
pub mod r_m1 {
    /// `forAll` -> `term_R_M1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_M1_forAll";
    /// `lhs` -> `term_R_M1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_M1_lhs";
    /// `rhs` -> `term_R_M1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_M1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Multiplicative identity: mul(x, 1) = x.
pub mod r_m2 {
    /// `forAll` -> `term_R_M2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_M2_forAll";
    /// `lhs` -> `term_R_M2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_M2_lhs";
    /// `rhs` -> `term_R_M2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_M2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Multiplicative commutativity: mul(x, y) = mul(y, x).
pub mod r_m3 {
    /// `forAll` -> `term_R_M3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_M3_forAll";
    /// `lhs` -> `term_R_M3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_M3_lhs";
    /// `rhs` -> `term_R_M3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_M3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Distributivity: mul(x, add(y, z)) = add(mul(x, y), mul(x, z)).
pub mod r_m4 {
    /// `forAll` -> `term_R_M4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_M4_forAll";
    /// `lhs` -> `term_R_M4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_M4_lhs";
    /// `rhs` -> `term_R_M4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_M4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Annihilation: mul(x, 0) = 0.
pub mod r_m5 {
    /// `forAll` -> `term_R_M5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_R_M5_forAll";
    /// `lhs` -> `term_R_M5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_R_M5_lhs";
    /// `rhs` -> `term_R_M5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_R_M5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Division right-identity: div(a, 1) = a.
pub mod dv_1 {
    /// `forAll` -> `term_DV_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DV_1_forAll";
    /// `lhs` -> `term_DV_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DV_1_lhs";
    /// `rhs` -> `term_DV_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DV_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Division left-absorbing: div(0, b) = 0 for b ≠ 0.
pub mod dv_2 {
    /// `forAll` -> `term_DV_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DV_2_forAll";
    /// `lhs` -> `term_DV_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DV_2_lhs";
    /// `rhs` -> `term_DV_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DV_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Division-of-multiplication recovery: div(mul(a, b), b) = a for b ≠ 0 in the unit cone.
pub mod dv_3 {
    /// `forAll` -> `term_DV_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DV_3_forAll";
    /// `lhs` -> `term_DV_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DV_3_lhs";
    /// `rhs` -> `term_DV_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DV_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Euclidean compatibility: a = add(mul(div(a, b), b), mod(a, b)) for b ≠ 0.
pub mod dv_4 {
    /// `forAll` -> `term_DV_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DV_4_forAll";
    /// `lhs` -> `term_DV_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DV_4_lhs";
    /// `rhs` -> `term_DV_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DV_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Zero exponent identity: pow(a, 0) = 1.
pub mod pw_1 {
    /// `forAll` -> `term_PW_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PW_1_forAll";
    /// `lhs` -> `term_PW_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PW_1_lhs";
    /// `rhs` -> `term_PW_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PW_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Unit exponent identity: pow(a, 1) = a.
pub mod pw_2 {
    /// `forAll` -> `term_PW_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PW_2_forAll";
    /// `lhs` -> `term_PW_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PW_2_lhs";
    /// `rhs` -> `term_PW_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PW_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Additive exponent decomposition: pow(a, add(b, c)) = mul(pow(a, b), pow(a, c)).
pub mod pw_3 {
    /// `forAll` -> `term_PW_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PW_3_forAll";
    /// `lhs` -> `term_PW_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PW_3_lhs";
    /// `rhs` -> `term_PW_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PW_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// XOR associativity: xor(x, xor(y, z)) = xor(xor(x, y), z).
pub mod b_1 {
    /// `forAll` -> `term_B_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_1_forAll";
    /// `lhs` -> `term_B_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_1_lhs";
    /// `rhs` -> `term_B_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// XOR identity: xor(x, 0) = x.
pub mod b_2 {
    /// `forAll` -> `term_B_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_2_forAll";
    /// `lhs` -> `term_B_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_2_lhs";
    /// `rhs` -> `term_B_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// XOR self-inverse: xor(x, x) = 0.
pub mod b_3 {
    /// `forAll` -> `term_B_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_3_forAll";
    /// `lhs` -> `term_B_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_3_lhs";
    /// `rhs` -> `term_B_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// AND associativity: and(x, and(y, z)) = and(and(x, y), z).
pub mod b_4 {
    /// `forAll` -> `term_B_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_4_forAll";
    /// `lhs` -> `term_B_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_4_lhs";
    /// `rhs` -> `term_B_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// AND identity: and(x, 2^n - 1) = x.
pub mod b_5 {
    /// `forAll` -> `term_B_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_5_forAll";
    /// `lhs` -> `term_B_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_5_lhs";
    /// `rhs` -> `term_B_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// AND annihilation: and(x, 0) = 0.
pub mod b_6 {
    /// `forAll` -> `term_B_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_6_forAll";
    /// `lhs` -> `term_B_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_6_lhs";
    /// `rhs` -> `term_B_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// OR associativity: or(x, or(y, z)) = or(or(x, y), z).
pub mod b_7 {
    /// `forAll` -> `term_B_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_7_forAll";
    /// `lhs` -> `term_B_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_7_lhs";
    /// `rhs` -> `term_B_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_7_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// OR identity: or(x, 0) = x.
pub mod b_8 {
    /// `forAll` -> `term_B_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_8_forAll";
    /// `lhs` -> `term_B_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_8_lhs";
    /// `rhs` -> `term_B_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_8_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Absorption: and(x, or(x, y)) = x.
pub mod b_9 {
    /// `forAll` -> `term_B_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_9_forAll";
    /// `lhs` -> `term_B_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_9_lhs";
    /// `rhs` -> `term_B_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_9_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// AND distributes over OR: and(x, or(y, z)) = or(and(x, y), and(x, z)).
pub mod b_10 {
    /// `forAll` -> `term_B_10_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_10_forAll";
    /// `lhs` -> `term_B_10_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_10_lhs";
    /// `rhs` -> `term_B_10_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_10_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// De Morgan 1: bnot(and(x, y)) = or(bnot(x), bnot(y)).
pub mod b_11 {
    /// `forAll` -> `term_B_11_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_11_forAll";
    /// `lhs` -> `term_B_11_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_11_lhs";
    /// `rhs` -> `term_B_11_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_11_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// De Morgan 2: bnot(or(x, y)) = and(bnot(x), bnot(y)).
pub mod b_12 {
    /// `forAll` -> `term_B_12_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_12_forAll";
    /// `lhs` -> `term_B_12_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_12_lhs";
    /// `rhs` -> `term_B_12_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_12_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Bnot involution: bnot(bnot(x)) = x.
pub mod b_13 {
    /// `forAll` -> `term_B_13_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_B_13_forAll";
    /// `lhs` -> `term_B_13_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_B_13_lhs";
    /// `rhs` -> `term_B_13_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_B_13_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Neg via subtraction: neg(x) = sub(0, x).
pub mod x_1 {
    /// `forAll` -> `term_X_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_X_1_forAll";
    /// `lhs` -> `term_X_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_X_1_lhs";
    /// `rhs` -> `term_X_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_X_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Complement via XOR: bnot(x) = xor(x, 2^n - 1).
pub mod x_2 {
    /// `forAll` -> `term_X_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_X_2_forAll";
    /// `lhs` -> `term_X_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_X_2_lhs";
    /// `rhs` -> `term_X_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_X_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Succ via addition: succ(x) = add(x, 1).
pub mod x_3 {
    /// `forAll` -> `term_X_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_X_3_forAll";
    /// `lhs` -> `term_X_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_X_3_lhs";
    /// `rhs` -> `term_X_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_X_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Pred via subtraction: pred(x) = sub(x, 1).
pub mod x_4 {
    /// `forAll` -> `term_X_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_X_4_forAll";
    /// `lhs` -> `term_X_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_X_4_lhs";
    /// `rhs` -> `term_X_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_X_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Neg-bnot bridge: neg(x) = add(bnot(x), 1).
pub mod x_5 {
    /// `forAll` -> `term_X_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_X_5_forAll";
    /// `lhs` -> `term_X_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_X_5_lhs";
    /// `rhs` -> `term_X_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_X_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Complement predecessor: bnot(x) = pred(neg(x)).
pub mod x_6 {
    /// `forAll` -> `term_X_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_X_6_forAll";
    /// `lhs` -> `term_X_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_X_6_lhs";
    /// `rhs` -> `term_X_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_X_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// XOR-add bridge: xor(x, y) = add(x, y) - 2 * and(x, y) (in Z before mod).
pub mod x_7 {
    /// `forAll` -> `term_X_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_X_7_forAll";
    /// `lhs` -> `term_X_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_X_7_lhs";
    /// `rhs` -> `term_X_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_X_7_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Rotation order: succ^\[2^n\](x) = x.
pub mod d_1 {
    /// `forAll` -> `term_D_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_D_1_forAll";
    /// `lhs` -> `term_D_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_D_1_lhs";
    /// `rhs` -> `term_D_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_D_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Conjugation: neg(succ(neg(x))) = pred(x).
pub mod d_3 {
    /// `forAll` -> `term_D_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_D_3_forAll";
    /// `lhs` -> `term_D_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_D_3_lhs";
    /// `rhs` -> `term_D_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_D_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Reverse composition: bnot(neg(x)) = pred(x).
pub mod d_4 {
    /// `forAll` -> `term_D_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_D_4_forAll";
    /// `lhs` -> `term_D_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_D_4_lhs";
    /// `rhs` -> `term_D_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_D_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Group closure: D_\[2^n\] = \[succ^k, neg ∘ succ^k : 0 ≤ k < 2^n\].
pub mod d_5 {
    /// `forAll` -> `term_D_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_D_5_forAll";
    /// `lhs` -> `term_D_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_D_5_lhs";
    /// `rhs` -> `term_D_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_D_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Unit group decomposition: R_n× ≅ Z/2 × Z/2^\[n-2\] for n ≥ 3.
pub mod u_1 {
    /// `forAll` -> `term_U_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_U_1_forAll";
    /// `lhs` -> `term_U_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_U_1_lhs";
    /// `rhs` -> `term_U_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_U_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Unit group special cases: R_1× ≅ \[1\]; R_2× ≅ Z/2.
pub mod u_2 {
    /// `forAll` -> `term_U_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_U_2_forAll";
    /// `lhs` -> `term_U_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_U_2_lhs";
    /// `rhs` -> `term_U_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_U_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Multiplicative order: ord(u) = lcm(ord((-1)^a), ord(3^b)).
pub mod u_3 {
    /// `forAll` -> `term_U_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_U_3_forAll";
    /// `lhs` -> `term_U_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_U_3_lhs";
    /// `rhs` -> `term_U_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_U_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Resonance period: ord_g(2) divides φ(g).
pub mod u_4 {
    /// `forAll` -> `term_U_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_U_4_forAll";
    /// `lhs` -> `term_U_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_U_4_lhs";
    /// `rhs` -> `term_U_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_U_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Step formula derivation: step_g = 2 * ((g - (2^n mod g)) mod g) + 1.
pub mod u_5 {
    /// `forAll` -> `term_U_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_U_5_forAll";
    /// `lhs` -> `term_U_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_U_5_lhs";
    /// `rhs` -> `term_U_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_U_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Scaling not dihedral: μ_u ∉ D_\[2^n\] for u ≠ ±1.
pub mod ag_1 {
    /// `forAll` -> `term_AG_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AG_1_forAll";
    /// `lhs` -> `term_AG_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AG_1_lhs";
    /// `rhs` -> `term_AG_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AG_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Affine group: Aff(R_n) = R_n× ⋉ R_n.
pub mod ag_2 {
    /// `forAll` -> `term_AG_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AG_2_forAll";
    /// `lhs` -> `term_AG_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AG_2_lhs";
    /// `rhs` -> `term_AG_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AG_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Affine group order: |Aff(R_n)| = 2^\[2n-1\].
pub mod ag_3 {
    /// `forAll` -> `term_AG_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AG_3_forAll";
    /// `lhs` -> `term_AG_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AG_3_lhs";
    /// `rhs` -> `term_AG_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AG_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Subgroup inclusion: D_\[2^n\] ⊂ Aff(R_n) with u ∈ \[±1\].
pub mod ag_4 {
    /// `forAll` -> `term_AG_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AG_4_forAll";
    /// `lhs` -> `term_AG_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AG_4_lhs";
    /// `rhs` -> `term_AG_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AG_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Addition decomposition: add(x,y)_k = xor(x_k, xor(y_k, c_k(x,y))).
pub mod ca_1 {
    /// `forAll` -> `term_CA_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CA_1_forAll";
    /// `lhs` -> `term_CA_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CA_1_lhs";
    /// `rhs` -> `term_CA_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CA_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry recurrence: c_\[k+1\](x,y) = or(and(x_k,y_k), and(xor(x_k,y_k), c_k)).
pub mod ca_2 {
    /// `forAll` -> `term_CA_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CA_2_forAll";
    /// `lhs` -> `term_CA_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CA_2_lhs";
    /// `rhs` -> `term_CA_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CA_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry commutativity: c(x, y) = c(y, x).
pub mod ca_3 {
    /// `forAll` -> `term_CA_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CA_3_forAll";
    /// `lhs` -> `term_CA_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CA_3_lhs";
    /// `rhs` -> `term_CA_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CA_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Zero carry: c(x, 0) = 0 at all positions.
pub mod ca_4 {
    /// `forAll` -> `term_CA_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CA_4_forAll";
    /// `lhs` -> `term_CA_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CA_4_lhs";
    /// `rhs` -> `term_CA_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CA_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Negation carry: c(x, neg(x))_k = 1 for k > v_2(x).
pub mod ca_5 {
    /// `forAll` -> `term_CA_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CA_5_forAll";
    /// `lhs` -> `term_CA_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CA_5_lhs";
    /// `rhs` -> `term_CA_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CA_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry-incompatibility link: d_Δ(x, y) > 0 iff ∃ k : c_k(x,y) = 1.
pub mod ca_6 {
    /// `forAll` -> `term_CA_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CA_6_forAll";
    /// `lhs` -> `term_CA_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CA_6_lhs";
    /// `rhs` -> `term_CA_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CA_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint pin union: pins of a composite constraint equal the union of component pins.
pub mod c_1 {
    /// `forAll` -> `term_C_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_C_1_forAll";
    /// `lhs` -> `term_C_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_C_1_lhs";
    /// `rhs` -> `term_C_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_C_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint composition commutativity.
pub mod c_2 {
    /// `forAll` -> `term_C_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_C_2_forAll";
    /// `lhs` -> `term_C_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_C_2_lhs";
    /// `rhs` -> `term_C_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_C_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint composition associativity.
pub mod c_3 {
    /// `forAll` -> `term_C_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_C_3_forAll";
    /// `lhs` -> `term_C_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_C_3_lhs";
    /// `rhs` -> `term_C_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_C_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint composition idempotence.
pub mod c_4 {
    /// `forAll` -> `term_C_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_C_4_forAll";
    /// `lhs` -> `term_C_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_C_4_lhs";
    /// `rhs` -> `term_C_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_C_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint composition identity element.
pub mod c_5 {
    /// `forAll` -> `term_C_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_C_5_forAll";
    /// `lhs` -> `term_C_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_C_5_lhs";
    /// `rhs` -> `term_C_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_C_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint composition annihilator.
pub mod c_6 {
    /// `forAll` -> `term_C_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_C_6_forAll";
    /// `lhs` -> `term_C_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_C_6_lhs";
    /// `rhs` -> `term_C_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_C_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint-depth invariant: carry complexity of the residue representation equals the type depth.
pub mod cdi {
    /// `forAll` -> `term_CDI_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CDI_forAll";
    /// `lhs` -> `term_CDI_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CDI_lhs";
    /// `rhs` -> `term_CDI_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CDI_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint quotient lattice isomorphism to power set.
pub mod cl_1 {
    /// `forAll` -> `term_CL_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CL_1_forAll";
    /// `lhs` -> `term_CL_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CL_1_lhs";
    /// `rhs` -> `term_CL_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CL_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Lattice join equals constraint composition.
pub mod cl_2 {
    /// `forAll` -> `term_CL_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CL_2_forAll";
    /// `lhs` -> `term_CL_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CL_2_lhs";
    /// `rhs` -> `term_CL_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CL_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Lattice meet pins the intersection of component pins.
pub mod cl_3 {
    /// `forAll` -> `term_CL_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CL_3_forAll";
    /// `lhs` -> `term_CL_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CL_3_lhs";
    /// `rhs` -> `term_CL_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CL_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint lattice distributivity.
pub mod cl_4 {
    /// `forAll` -> `term_CL_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CL_4_forAll";
    /// `lhs` -> `term_CL_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CL_4_lhs";
    /// `rhs` -> `term_CL_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CL_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint lattice complement existence.
pub mod cl_5 {
    /// `forAll` -> `term_CL_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CL_5_forAll";
    /// `lhs` -> `term_CL_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CL_5_lhs";
    /// `rhs` -> `term_CL_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CL_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Constraint redundancy criterion.
pub mod cm_1 {
    /// `forAll` -> `term_CM_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CM_1_forAll";
    /// `lhs` -> `term_CM_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CM_1_lhs";
    /// `rhs` -> `term_CM_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CM_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Minimal cover via greedy irredundant removal.
pub mod cm_2 {
    /// `forAll` -> `term_CM_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CM_2_forAll";
    /// `lhs` -> `term_CM_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CM_2_lhs";
    /// `rhs` -> `term_CM_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CM_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Minimum constraint count to cover n sites.
pub mod cm_3 {
    /// `forAll` -> `term_CM_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CM_3_forAll";
    /// `lhs` -> `term_CM_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CM_3_lhs";
    /// `rhs` -> `term_CM_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CM_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Residue constraint cost is the step formula.
pub mod cr_1 {
    /// `forAll` -> `term_CR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CR_1_forAll";
    /// `lhs` -> `term_CR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CR_1_lhs";
    /// `rhs` -> `term_CR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CR_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry constraint cost is the popcount of the pattern.
pub mod cr_2 {
    /// `forAll` -> `term_CR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CR_2_forAll";
    /// `lhs` -> `term_CR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CR_2_lhs";
    /// `rhs` -> `term_CR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CR_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Depth constraint cost is sum of residue and carry costs.
pub mod cr_3 {
    /// `forAll` -> `term_CR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CR_3_forAll";
    /// `lhs` -> `term_CR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CR_3_lhs";
    /// `rhs` -> `term_CR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CR_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Composite constraint cost is subadditive.
pub mod cr_4 {
    /// `forAll` -> `term_CR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CR_4_forAll";
    /// `lhs` -> `term_CR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CR_4_lhs";
    /// `rhs` -> `term_CR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CR_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Optimal resolution order is increasing cost.
pub mod cr_5 {
    /// `forAll` -> `term_CR_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CR_5_forAll";
    /// `lhs` -> `term_CR_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CR_5_lhs";
    /// `rhs` -> `term_CR_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CR_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site monotonicity: a pinned site cannot be unpinned.
pub mod f_1 {
    /// `forAll` -> `term_F_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_F_1_forAll";
    /// `lhs` -> `term_F_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_F_1_lhs";
    /// `rhs` -> `term_F_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_F_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site budget upper bound: at most n pin operations to close.
pub mod f_2 {
    /// `forAll` -> `term_F_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_F_2_forAll";
    /// `lhs` -> `term_F_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_F_2_lhs";
    /// `rhs` -> `term_F_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_F_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site budget conservation: pinned + free = total sites.
pub mod f_3 {
    /// `forAll` -> `term_F_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_F_3_forAll";
    /// `lhs` -> `term_F_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_F_3_lhs";
    /// `rhs` -> `term_F_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_F_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site budget closure: closed iff all sites pinned.
pub mod f_4 {
    /// `forAll` -> `term_F_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_F_4_forAll";
    /// `lhs` -> `term_F_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_F_4_lhs";
    /// `rhs` -> `term_F_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_F_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site lattice bottom: all sites free.
pub mod fl_1 {
    /// `forAll` -> `term_FL_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FL_1_forAll";
    /// `lhs` -> `term_FL_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FL_1_lhs";
    /// `rhs` -> `term_FL_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FL_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site lattice top: all sites pinned.
pub mod fl_2 {
    /// `forAll` -> `term_FL_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FL_2_forAll";
    /// `lhs` -> `term_FL_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FL_2_lhs";
    /// `rhs` -> `term_FL_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FL_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site lattice join is union of pinnings.
pub mod fl_3 {
    /// `forAll` -> `term_FL_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FL_3_forAll";
    /// `lhs` -> `term_FL_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FL_3_lhs";
    /// `rhs` -> `term_FL_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FL_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site lattice height equals n.
pub mod fl_4 {
    /// `forAll` -> `term_FL_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FL_4_forAll";
    /// `lhs` -> `term_FL_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FL_4_lhs";
    /// `rhs` -> `term_FL_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FL_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Unit partition membership: x is a unit iff site_0(x) = 1 (x is odd).
pub mod fpm_1 {
    /// `forAll` -> `term_FPM_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_1_forAll";
    /// `lhs` -> `term_FPM_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_1_lhs";
    /// `rhs` -> `term_FPM_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Exterior partition membership: x is exterior iff x is not in the carrier of T.
pub mod fpm_2 {
    /// `forAll` -> `term_FPM_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_2_forAll";
    /// `lhs` -> `term_FPM_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_2_lhs";
    /// `rhs` -> `term_FPM_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Irreducible partition membership: x is irreducible iff x is not a unit, exterior, or reducible.
pub mod fpm_3 {
    /// `forAll` -> `term_FPM_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_3_forAll";
    /// `lhs` -> `term_FPM_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_3_lhs";
    /// `rhs` -> `term_FPM_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Reducible partition membership: x is reducible iff x is not a unit, exterior, or irreducible.
pub mod fpm_4 {
    /// `forAll` -> `term_FPM_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_4_forAll";
    /// `lhs` -> `term_FPM_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_4_lhs";
    /// `rhs` -> `term_FPM_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// 2-adic decomposition: every element factors as 2^{v(x)} times an odd unit.
pub mod fpm_5 {
    /// `forAll` -> `term_FPM_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_5_forAll";
    /// `lhs` -> `term_FPM_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_5_lhs";
    /// `rhs` -> `term_FPM_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Stratum size formula.
pub mod fpm_6 {
    /// `forAll` -> `term_FPM_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_6_forAll";
    /// `lhs` -> `term_FPM_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_6_lhs";
    /// `rhs` -> `term_FPM_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Base type partition cardinalities.
pub mod fpm_7 {
    /// `forAll` -> `term_FPM_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_7_forAll";
    /// `lhs` -> `term_FPM_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_7_lhs";
    /// `rhs` -> `term_FPM_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_7_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site extraction: site_k(x) is the k-th bit of x.
pub mod fs_1 {
    /// `forAll` -> `term_FS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FS_1_forAll";
    /// `lhs` -> `term_FS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FS_1_lhs";
    /// `rhs` -> `term_FS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FS_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site 0 is parity.
pub mod fs_2 {
    /// `forAll` -> `term_FS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FS_2_forAll";
    /// `lhs` -> `term_FS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FS_2_lhs";
    /// `rhs` -> `term_FS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FS_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Progressive site determination: site_k given lower sites determines x mod 2^{k+1}.
pub mod fs_3 {
    /// `forAll` -> `term_FS_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FS_3_forAll";
    /// `lhs` -> `term_FS_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FS_3_lhs";
    /// `rhs` -> `term_FS_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FS_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Cumulative site determination: sites 0..k together determine x mod 2^{k+1}.
pub mod fs_4 {
    /// `forAll` -> `term_FS_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FS_4_forAll";
    /// `lhs` -> `term_FS_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FS_4_lhs";
    /// `rhs` -> `term_FS_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FS_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Complete site determination: all n sites determine x uniquely.
pub mod fs_5 {
    /// `forAll` -> `term_FS_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FS_5_forAll";
    /// `lhs` -> `term_FS_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FS_5_lhs";
    /// `rhs` -> `term_FS_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FS_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Stratum from sites: v_2(x) is the minimum k where site_k(x) = 1.
pub mod fs_6 {
    /// `forAll` -> `term_FS_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FS_6_forAll";
    /// `lhs` -> `term_FS_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FS_6_lhs";
    /// `rhs` -> `term_FS_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FS_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Depth bound: depth(x) ≤ v_2(x) for irreducible elements.
pub mod fs_7 {
    /// `forAll` -> `term_FS_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FS_7_forAll";
    /// `lhs` -> `term_FS_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FS_7_lhs";
    /// `rhs` -> `term_FS_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FS_7_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Resolution strategy equivalence: dihedral, canonical-form, and evaluation resolvers all compute the same partition.
pub mod re_1 {
    /// `forAll` -> `term_RE_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RE_1_forAll";
    /// `lhs` -> `term_RE_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RE_1_lhs";
    /// `rhs` -> `term_RE_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RE_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Resolution monotonicity: pinned count never decreases.
pub mod ir_1 {
    /// `forAll` -> `term_IR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IR_1_forAll";
    /// `lhs` -> `term_IR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IR_1_lhs";
    /// `rhs` -> `term_IR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IR_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Resolution convergence bound: at most n iterations.
pub mod ir_2 {
    /// `forAll` -> `term_IR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IR_2_forAll";
    /// `lhs` -> `term_IR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IR_2_lhs";
    /// `rhs` -> `term_IR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IR_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Convergence rate definition.
pub mod ir_3 {
    /// `forAll` -> `term_IR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IR_3_forAll";
    /// `lhs` -> `term_IR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IR_3_lhs";
    /// `rhs` -> `term_IR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IR_3_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Resolution termination: loop terminates if constraint set spans all sites.
pub mod ir_4 {
    /// `forAll` -> `term_IR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IR_4_forAll";
    /// `lhs` -> `term_IR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IR_4_lhs";
    /// `rhs` -> `term_IR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IR_4_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Optimal resolution level for a factor: n ≡ 0 (mod ord_g(2)).
pub mod sf_1 {
    /// `forAll` -> `term_SF_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SF_1_forAll";
    /// `lhs` -> `term_SF_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SF_1_lhs";
    /// `rhs` -> `term_SF_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SF_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Constraint ordering by step cost: smaller step_g first.
pub mod sf_2 {
    /// `forAll` -> `term_SF_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SF_2_forAll";
    /// `lhs` -> `term_SF_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SF_2_lhs";
    /// `rhs` -> `term_SF_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SF_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Resolution determinism: same type and constraint sequence yield unique partition.
pub mod rd_1 {
    /// `forAll` -> `term_RD_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RD_1_forAll";
    /// `lhs` -> `term_RD_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RD_1_lhs";
    /// `rhs` -> `term_RD_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RD_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Order independence: complete constraint sets yield the same partition regardless of order.
pub mod rd_2 {
    /// `forAll` -> `term_RD_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RD_2_forAll";
    /// `lhs` -> `term_RD_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RD_2_lhs";
    /// `rhs` -> `term_RD_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RD_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Evaluation resolver directly computes the set-theoretic partition.
pub mod se_1 {
    /// `forAll` -> `term_SE_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SE_1_forAll";
    /// `lhs` -> `term_SE_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SE_1_lhs";
    /// `rhs` -> `term_SE_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SE_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Dihedral factorization resolver yields the same partition via orbit decomposition.
pub mod se_2 {
    /// `forAll` -> `term_SE_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SE_2_forAll";
    /// `lhs` -> `term_SE_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SE_2_lhs";
    /// `rhs` -> `term_SE_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SE_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Canonical form resolver yields the same partition via confluent rewrite.
pub mod se_3 {
    /// `forAll` -> `term_SE_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SE_3_forAll";
    /// `lhs` -> `term_SE_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SE_3_lhs";
    /// `rhs` -> `term_SE_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SE_3_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// All three strategies compute the same set-theoretic partition.
pub mod se_4 {
    /// `forAll` -> `term_SE_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SE_4_forAll";
    /// `lhs` -> `term_SE_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SE_4_lhs";
    /// `rhs` -> `term_SE_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SE_4_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Benefit of a constraint is the number of new pins it provides.
pub mod oo_1 {
    /// `forAll` -> `term_OO_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OO_1_forAll";
    /// `lhs` -> `term_OO_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OO_1_lhs";
    /// `rhs` -> `term_OO_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OO_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Constraint cost is step or popcount depending on type.
pub mod oo_2 {
    /// `forAll` -> `term_OO_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OO_2_forAll";
    /// `lhs` -> `term_OO_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OO_2_lhs";
    /// `rhs` -> `term_OO_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OO_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Greedy selection maximizes benefit-to-cost ratio.
pub mod oo_3 {
    /// `forAll` -> `term_OO_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OO_3_forAll";
    /// `lhs` -> `term_OO_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OO_3_lhs";
    /// `rhs` -> `term_OO_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OO_3_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Greedy approximation achieves (1 − 1/e) ≈ 63% of optimal.
pub mod oo_4 {
    /// `forAll` -> `term_OO_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OO_4_forAll";
    /// `lhs` -> `term_OO_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OO_4_lhs";
    /// `rhs` -> `term_OO_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OO_4_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Tiebreaker: prefer vertical (residue) before horizontal (carry).
pub mod oo_5 {
    /// `forAll` -> `term_OO_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OO_5_forAll";
    /// `lhs` -> `term_OO_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OO_5_lhs";
    /// `rhs` -> `term_OO_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OO_5_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Minimum convergence rate: 1 site per iteration (worst case).
pub mod cb_1 {
    /// `forAll` -> `term_CB_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CB_1_forAll";
    /// `lhs` -> `term_CB_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CB_1_lhs";
    /// `rhs` -> `term_CB_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CB_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Maximum convergence rate: n sites in 1 iteration (best case).
pub mod cb_2 {
    /// `forAll` -> `term_CB_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CB_2_forAll";
    /// `lhs` -> `term_CB_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CB_2_lhs";
    /// `rhs` -> `term_CB_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CB_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Expected residue constraint rate: ⌊log_2(m)⌋ sites per constraint.
pub mod cb_3 {
    /// `forAll` -> `term_CB_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CB_3_forAll";
    /// `lhs` -> `term_CB_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CB_3_lhs";
    /// `rhs` -> `term_CB_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CB_3_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stall detection: convergenceRate < 1 for 2 iterations suggests insufficiency.
pub mod cb_4 {
    /// `forAll` -> `term_CB_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CB_4_forAll";
    /// `lhs` -> `term_CB_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CB_4_lhs";
    /// `rhs` -> `term_CB_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CB_4_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Sufficiency criterion: pin union covers all site positions.
pub mod cb_5 {
    /// `forAll` -> `term_CB_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CB_5_forAll";
    /// `lhs` -> `term_CB_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CB_5_lhs";
    /// `rhs` -> `term_CB_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CB_5_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Iteration bound for k constraints: at most min(k, n) iterations.
pub mod cb_6 {
    /// `forAll` -> `term_CB_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CB_6_forAll";
    /// `lhs` -> `term_CB_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CB_6_lhs";
    /// `rhs` -> `term_CB_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CB_6_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Ring metric triangle inequality.
pub mod ob_m1 {
    /// `forAll` -> `term_OB_M1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_M1_forAll";
    /// `lhs` -> `term_OB_M1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_M1_lhs";
    /// `rhs` -> `term_OB_M1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_M1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Hamming metric triangle inequality.
pub mod ob_m2 {
    /// `forAll` -> `term_OB_M2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_M2_forAll";
    /// `lhs` -> `term_OB_M2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_M2_lhs";
    /// `rhs` -> `term_OB_M2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_M2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Incompatibility metric is the absolute difference of ring and Hamming metrics.
pub mod ob_m3 {
    /// `forAll` -> `term_OB_M3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_M3_forAll";
    /// `lhs` -> `term_OB_M3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_M3_lhs";
    /// `rhs` -> `term_OB_M3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_M3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Negation preserves ring metric.
pub mod ob_m4 {
    /// `forAll` -> `term_OB_M4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_M4_forAll";
    /// `lhs` -> `term_OB_M4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_M4_lhs";
    /// `rhs` -> `term_OB_M4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_M4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Bitwise complement preserves Hamming metric.
pub mod ob_m5 {
    /// `forAll` -> `term_OB_M5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_M5_forAll";
    /// `lhs` -> `term_OB_M5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_M5_lhs";
    /// `rhs` -> `term_OB_M5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_M5_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Successor preserves ring metric but may change Hamming metric.
pub mod ob_m6 {
    /// `forAll` -> `term_OB_M6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_M6_forAll";
    /// `lhs` -> `term_OB_M6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_M6_lhs";
    /// `rhs` -> `term_OB_M6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_M6_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Negation-complement commutator is constant 2.
pub mod ob_c1 {
    /// `forAll` -> `term_OB_C1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_C1_forAll";
    /// `lhs` -> `term_OB_C1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_C1_lhs";
    /// `rhs` -> `term_OB_C1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_C1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Negation-translation commutator.
pub mod ob_c2 {
    /// `forAll` -> `term_OB_C2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_C2_forAll";
    /// `lhs` -> `term_OB_C2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_C2_lhs";
    /// `rhs` -> `term_OB_C2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_C2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Complement-XOR commutator is trivial.
pub mod ob_c3 {
    /// `forAll` -> `term_OB_C3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_C3_forAll";
    /// `lhs` -> `term_OB_C3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_C3_lhs";
    /// `rhs` -> `term_OB_C3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_C3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Additive paths have trivial monodromy (abelian ⇒ path-independent).
pub mod ob_h1 {
    /// `forAll` -> `term_OB_H1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_H1_forAll";
    /// `lhs` -> `term_OB_H1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_H1_lhs";
    /// `rhs` -> `term_OB_H1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_H1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Dihedral generator paths have monodromy in D_{2^n}.
pub mod ob_h2 {
    /// `forAll` -> `term_OB_H2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_H2_forAll";
    /// `lhs` -> `term_OB_H2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_H2_lhs";
    /// `rhs` -> `term_OB_H2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_H2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Successor-only closed path winding number.
pub mod ob_h3 {
    /// `forAll` -> `term_OB_H3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_H3_forAll";
    /// `lhs` -> `term_OB_H3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_H3_lhs";
    /// `rhs` -> `term_OB_H3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_H3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Path length is additive under concatenation.
pub mod ob_p1 {
    /// `forAll` -> `term_OB_P1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_P1_forAll";
    /// `lhs` -> `term_OB_P1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_P1_lhs";
    /// `rhs` -> `term_OB_P1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_P1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Total variation is subadditive under concatenation.
pub mod ob_p2 {
    /// `forAll` -> `term_OB_P2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_P2_forAll";
    /// `lhs` -> `term_OB_P2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_P2_lhs";
    /// `rhs` -> `term_OB_P2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_P2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Reduction length is additive under sequential composition.
pub mod ob_p3 {
    /// `forAll` -> `term_OB_P3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OB_P3_forAll";
    /// `lhs` -> `term_OB_P3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OB_P3_lhs";
    /// `rhs` -> `term_OB_P3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OB_P3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Catastrophe boundaries are powers of 2.
pub mod ct_1 {
    /// `forAll` -> `term_CT_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CT_1_forAll";
    /// `lhs` -> `term_CT_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CT_1_lhs";
    /// `rhs` -> `term_CT_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CT_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Odd prime catastrophe transitions visibility via residue constraints.
pub mod ct_2 {
    /// `forAll` -> `term_CT_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CT_2_forAll";
    /// `lhs` -> `term_CT_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CT_2_lhs";
    /// `rhs` -> `term_CT_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CT_2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Catastrophe threshold is normalized step cost.
pub mod ct_3 {
    /// `forAll` -> `term_CT_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CT_3_forAll";
    /// `lhs` -> `term_CT_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CT_3_lhs";
    /// `rhs` -> `term_CT_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CT_3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Composite catastrophe threshold is max of component thresholds.
pub mod ct_4 {
    /// `forAll` -> `term_CT_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CT_4_forAll";
    /// `lhs` -> `term_CT_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CT_4_lhs";
    /// `rhs` -> `term_CT_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CT_4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Curvature flux is the sum of incompatibility along a path.
pub mod cf_1 {
    /// `forAll` -> `term_CF_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CF_1_forAll";
    /// `lhs` -> `term_CF_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CF_1_lhs";
    /// `rhs` -> `term_CF_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CF_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Resolution cost is bounded below by curvature flux of optimal path.
pub mod cf_2 {
    /// `forAll` -> `term_CF_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CF_2_forAll";
    /// `lhs` -> `term_CF_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CF_2_lhs";
    /// `rhs` -> `term_CF_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CF_2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Successor curvature flux: trailing_ones(x) for most x, n−1 at maximum.
pub mod cf_3 {
    /// `forAll` -> `term_CF_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CF_3_forAll";
    /// `lhs` -> `term_CF_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CF_3_lhs";
    /// `rhs` -> `term_CF_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CF_3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Total successor curvature flux over R_n equals 2^n − 2.
pub mod cf_4 {
    /// `forAll` -> `term_CF_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CF_4_forAll";
    /// `lhs` -> `term_CF_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CF_4_lhs";
    /// `rhs` -> `term_CF_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CF_4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Additive holonomy is trivial (abelian group).
pub mod hg_1 {
    /// `forAll` -> `term_HG_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HG_1_forAll";
    /// `lhs` -> `term_HG_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HG_1_lhs";
    /// `rhs` -> `term_HG_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HG_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Dihedral generator holonomy group is D_{2^n}.
pub mod hg_2 {
    /// `forAll` -> `term_HG_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HG_2_forAll";
    /// `lhs` -> `term_HG_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HG_2_lhs";
    /// `rhs` -> `term_HG_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HG_2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Unit multiplication holonomy equals the unit group.
pub mod hg_3 {
    /// `forAll` -> `term_HG_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HG_3_forAll";
    /// `lhs` -> `term_HG_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HG_3_lhs";
    /// `rhs` -> `term_HG_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HG_3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Full holonomy group is the affine group.
pub mod hg_4 {
    /// `forAll` -> `term_HG_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HG_4_forAll";
    /// `lhs` -> `term_HG_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HG_4_lhs";
    /// `rhs` -> `term_HG_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HG_4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Holonomy group decomposition into dihedral and non-trivial units.
pub mod hg_5 {
    /// `forAll` -> `term_HG_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HG_5_forAll";
    /// `lhs` -> `term_HG_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HG_5_lhs";
    /// `rhs` -> `term_HG_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HG_5_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Category left identity: compose(id, f) = f.
pub mod t_c1 {
    /// `forAll` -> `term_T_C1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_C1_forAll";
    /// `lhs` -> `term_T_C1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_C1_lhs";
    /// `rhs` -> `term_T_C1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_C1_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Category right identity: compose(f, id) = f.
pub mod t_c2 {
    /// `forAll` -> `term_T_C2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_C2_forAll";
    /// `lhs` -> `term_T_C2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_C2_lhs";
    /// `rhs` -> `term_T_C2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_C2_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Category associativity of transform composition.
pub mod t_c3 {
    /// `forAll` -> `term_T_C3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_C3_forAll";
    /// `lhs` -> `term_T_C3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_C3_lhs";
    /// `rhs` -> `term_T_C3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_C3_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Composability condition: f composesWith g iff target(f) = source(g).
pub mod t_c4 {
    /// `forAll` -> `term_T_C4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_C4_forAll";
    /// `lhs` -> `term_T_C4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_C4_lhs";
    /// `rhs` -> `term_T_C4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_C4_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Negation is a ring-metric isometry.
pub mod t_i1 {
    /// `forAll` -> `term_T_I1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_I1_forAll";
    /// `lhs` -> `term_T_I1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_I1_lhs";
    /// `rhs` -> `term_T_I1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_I1_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Bitwise complement is a Hamming-metric isometry.
pub mod t_i2 {
    /// `forAll` -> `term_T_I2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_I2_forAll";
    /// `lhs` -> `term_T_I2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_I2_lhs";
    /// `rhs` -> `term_T_I2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_I2_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Successor as composed isometries: succ = neg ∘ bnot preserves d_R but not d_H.
pub mod t_i3 {
    /// `forAll` -> `term_T_I3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_I3_forAll";
    /// `lhs` -> `term_T_I3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_I3_lhs";
    /// `rhs` -> `term_T_I3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_I3_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Ring isometries form a group under composition.
pub mod t_i4 {
    /// `forAll` -> `term_T_I4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_I4_forAll";
    /// `lhs` -> `term_T_I4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_I4_lhs";
    /// `rhs` -> `term_T_I4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_I4_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// CurvatureObservable measures failure of ring isometry to be Hamming isometry.
pub mod t_i5 {
    /// `forAll` -> `term_T_I5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_I5_forAll";
    /// `lhs` -> `term_T_I5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_I5_lhs";
    /// `rhs` -> `term_T_I5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_I5_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding injectivity.
pub mod t_e1 {
    /// `forAll` -> `term_T_E1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_E1_forAll";
    /// `lhs` -> `term_T_E1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_E1_lhs";
    /// `rhs` -> `term_T_E1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_E1_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding is a ring homomorphism.
pub mod t_e2 {
    /// `forAll` -> `term_T_E2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_E2_forAll";
    /// `lhs` -> `term_T_E2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_E2_lhs";
    /// `rhs` -> `term_T_E2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_E2_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding transitivity: composition of embeddings is an embedding.
pub mod t_e3 {
    /// `forAll` -> `term_T_E3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_E3_forAll";
    /// `lhs` -> `term_T_E3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_E3_lhs";
    /// `rhs` -> `term_T_E3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_E3_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding address coherence: glyph ∘ ι ∘ addresses is well-defined.
pub mod t_e4 {
    /// `forAll` -> `term_T_E4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_E4_forAll";
    /// `lhs` -> `term_T_E4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_E4_lhs";
    /// `rhs` -> `term_T_E4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_E4_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Dihedral group acts on constraints by transforming them.
pub mod t_a1 {
    /// `forAll` -> `term_T_A1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_A1_forAll";
    /// `lhs` -> `term_T_A1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_A1_lhs";
    /// `rhs` -> `term_T_A1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_A1_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Dihedral group action on partitions permutes components.
pub mod t_a2 {
    /// `forAll` -> `term_T_A2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_A2_forAll";
    /// `lhs` -> `term_T_A2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_A2_lhs";
    /// `rhs` -> `term_T_A2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_A2_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Dihedral orbits determine irreducibility boundaries.
pub mod t_a3 {
    /// `forAll` -> `term_T_A3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_A3_forAll";
    /// `lhs` -> `term_T_A3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_A3_lhs";
    /// `rhs` -> `term_T_A3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_A3_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Fixed points of negation are {0, 2^{n−1}}; bnot has no fixed points.
pub mod t_a4 {
    /// `forAll` -> `term_T_A4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_T_A4_forAll";
    /// `lhs` -> `term_T_A4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_T_A4_lhs";
    /// `rhs` -> `term_T_A4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_T_A4_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Automorphism group consists of unit multiplications.
pub mod au_1 {
    /// `forAll` -> `term_AU_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AU_1_forAll";
    /// `lhs` -> `term_AU_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AU_1_lhs";
    /// `rhs` -> `term_AU_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AU_1_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Automorphism group is isomorphic to the unit group.
pub mod au_2 {
    /// `forAll` -> `term_AU_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AU_2_forAll";
    /// `lhs` -> `term_AU_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AU_2_lhs";
    /// `rhs` -> `term_AU_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AU_2_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Automorphism group order is 2^{n−1}.
pub mod au_3 {
    /// `forAll` -> `term_AU_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AU_3_forAll";
    /// `lhs` -> `term_AU_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AU_3_lhs";
    /// `rhs` -> `term_AU_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AU_3_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Intersection of automorphism group with dihedral group is {id, neg}.
pub mod au_4 {
    /// `forAll` -> `term_AU_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AU_4_forAll";
    /// `lhs` -> `term_AU_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AU_4_lhs";
    /// `rhs` -> `term_AU_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AU_4_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Affine group is generated by D_{2^n} and μ_3.
pub mod au_5 {
    /// `forAll` -> `term_AU_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AU_5_forAll";
    /// `lhs` -> `term_AU_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AU_5_lhs";
    /// `rhs` -> `term_AU_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AU_5_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding functor action on morphisms.
pub mod ef_1 {
    /// `forAll` -> `term_EF_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EF_1_forAll";
    /// `lhs` -> `term_EF_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EF_1_lhs";
    /// `rhs` -> `term_EF_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EF_1_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding functor preserves composition.
pub mod ef_2 {
    /// `forAll` -> `term_EF_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EF_2_forAll";
    /// `lhs` -> `term_EF_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EF_2_lhs";
    /// `rhs` -> `term_EF_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EF_2_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding functor preserves identities.
pub mod ef_3 {
    /// `forAll` -> `term_EF_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EF_3_forAll";
    /// `lhs` -> `term_EF_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EF_3_lhs";
    /// `rhs` -> `term_EF_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EF_3_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding functor composition is functorial.
pub mod ef_4 {
    /// `forAll` -> `term_EF_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EF_4_forAll";
    /// `lhs` -> `term_EF_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EF_4_lhs";
    /// `rhs` -> `term_EF_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EF_4_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding functor preserves ring isometries.
pub mod ef_5 {
    /// `forAll` -> `term_EF_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EF_5_forAll";
    /// `lhs` -> `term_EF_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EF_5_lhs";
    /// `rhs` -> `term_EF_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EF_5_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding functor maps dihedral subgroup into target dihedral group.
pub mod ef_6 {
    /// `forAll` -> `term_EF_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EF_6_forAll";
    /// `lhs` -> `term_EF_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EF_6_lhs";
    /// `rhs` -> `term_EF_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EF_6_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Embedding functor maps unit group into target unit group.
pub mod ef_7 {
    /// `forAll` -> `term_EF_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EF_7_forAll";
    /// `lhs` -> `term_EF_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EF_7_lhs";
    /// `rhs` -> `term_EF_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EF_7_rhs";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Braille glyph encoding: 6-bit blocks to Braille characters.
pub mod aa_1 {
    /// `forAll` -> `term_AA_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AA_1_forAll";
    /// `lhs` -> `term_AA_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AA_1_lhs";
    /// `rhs` -> `term_AA_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AA_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Braille XOR homomorphism: Braille encoding commutes with XOR.
pub mod aa_2 {
    /// `forAll` -> `term_AA_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AA_2_forAll";
    /// `lhs` -> `term_AA_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AA_2_lhs";
    /// `rhs` -> `term_AA_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AA_2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Braille complement: glyph of bnot(x) is character-wise complement of glyph(x).
pub mod aa_3 {
    /// `forAll` -> `term_AA_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AA_3_forAll";
    /// `lhs` -> `term_AA_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AA_3_lhs";
    /// `rhs` -> `term_AA_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AA_3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Addition does not lift to address space: no glyph homomorphism for add.
pub mod aa_4 {
    /// `forAll` -> `term_AA_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AA_4_forAll";
    /// `lhs` -> `term_AA_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AA_4_lhs";
    /// `rhs` -> `term_AA_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AA_4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Liftable operations are exactly the Boolean operations.
pub mod aa_5 {
    /// `forAll` -> `term_AA_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AA_5_forAll";
    /// `lhs` -> `term_AA_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AA_5_lhs";
    /// `rhs` -> `term_AA_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AA_5_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Negation decomposes into liftable bnot and non-liftable succ.
pub mod aa_6 {
    /// `forAll` -> `term_AA_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AA_6_forAll";
    /// `lhs` -> `term_AA_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AA_6_lhs";
    /// `rhs` -> `term_AA_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AA_6_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Address metric is sum of per-character Hamming distances.
pub mod am_1 {
    /// `forAll` -> `term_AM_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AM_1_forAll";
    /// `lhs` -> `term_AM_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AM_1_lhs";
    /// `rhs` -> `term_AM_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AM_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Address metric equals Hamming metric on ring elements.
pub mod am_2 {
    /// `forAll` -> `term_AM_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AM_2_forAll";
    /// `lhs` -> `term_AM_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AM_2_lhs";
    /// `rhs` -> `term_AM_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AM_2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Address metric does not preserve ring metric in general.
pub mod am_3 {
    /// `forAll` -> `term_AM_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AM_3_forAll";
    /// `lhs` -> `term_AM_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AM_3_lhs";
    /// `rhs` -> `term_AM_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AM_3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Address incompatibility metric.
pub mod am_4 {
    /// `forAll` -> `term_AM_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AM_4_forAll";
    /// `lhs` -> `term_AM_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AM_4_lhs";
    /// `rhs` -> `term_AM_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AM_4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Entropy of a site budget state.
pub mod th_1 {
    /// `forAll` -> `term_TH_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_1_forAll";
    /// `lhs` -> `term_TH_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_1_lhs";
    /// `rhs` -> `term_TH_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_1_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Maximum entropy: unconstrained state has S = n × ln 2.
pub mod th_2 {
    /// `forAll` -> `term_TH_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_2_forAll";
    /// `lhs` -> `term_TH_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_2_lhs";
    /// `rhs` -> `term_TH_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_2_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Zero entropy: fully resolved state has S = 0.
pub mod th_3 {
    /// `forAll` -> `term_TH_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_3_forAll";
    /// `lhs` -> `term_TH_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_3_lhs";
    /// `rhs` -> `term_TH_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_3_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Landauer bound on total resolution cost.
pub mod th_4 {
    /// `forAll` -> `term_TH_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_4_forAll";
    /// `lhs` -> `term_TH_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_4_lhs";
    /// `rhs` -> `term_TH_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_4_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Critical inverse temperature for UOR site system.
pub mod th_5 {
    /// `forAll` -> `term_TH_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_5_forAll";
    /// `lhs` -> `term_TH_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_5_lhs";
    /// `rhs` -> `term_TH_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_5_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Constraint application removes entropy; convergence rate equals cooling rate.
pub mod th_6 {
    /// `forAll` -> `term_TH_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_6_forAll";
    /// `lhs` -> `term_TH_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_6_lhs";
    /// `rhs` -> `term_TH_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_6_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// CatastropheThreshold is the temperature of a partition phase transition.
pub mod th_7 {
    /// `forAll` -> `term_TH_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_7_forAll";
    /// `lhs` -> `term_TH_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_7_lhs";
    /// `rhs` -> `term_TH_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_7_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Step formula as free-energy cost of a constraint boundary.
pub mod th_8 {
    /// `forAll` -> `term_TH_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_8_forAll";
    /// `lhs` -> `term_TH_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_8_lhs";
    /// `rhs` -> `term_TH_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_8_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Computational hardness maps to type incompleteness (high temperature).
pub mod th_9 {
    /// `forAll` -> `term_TH_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_9_forAll";
    /// `lhs` -> `term_TH_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_9_lhs";
    /// `rhs` -> `term_TH_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_9_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Type resolution is measurement; cost ≥ entropy removed.
pub mod th_10 {
    /// `forAll` -> `term_TH_10_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TH_10_forAll";
    /// `lhs` -> `term_TH_10_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TH_10_lhs";
    /// `rhs` -> `term_TH_10_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TH_10_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Adiabatic schedule: decreasing freeRank, cost-per-site ordering.
pub mod ar_1 {
    /// `forAll` -> `term_AR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AR_1_forAll";
    /// `lhs` -> `term_AR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AR_1_lhs";
    /// `rhs` -> `term_AR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AR_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Adiabatic cost is sum of constraint costs in optimal order.
pub mod ar_2 {
    /// `forAll` -> `term_AR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AR_2_forAll";
    /// `lhs` -> `term_AR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AR_2_lhs";
    /// `rhs` -> `term_AR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AR_2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Adiabatic cost satisfies Landauer bound.
pub mod ar_3 {
    /// `forAll` -> `term_AR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AR_3_forAll";
    /// `lhs` -> `term_AR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AR_3_lhs";
    /// `rhs` -> `term_AR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AR_3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Adiabatic efficiency η ≤ 1.
pub mod ar_4 {
    /// `forAll` -> `term_AR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AR_4_forAll";
    /// `lhs` -> `term_AR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AR_4_lhs";
    /// `rhs` -> `term_AR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AR_4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Greedy vs adiabatic cost difference: ≤ 5% for n ≤ 16.
pub mod ar_5 {
    /// `forAll` -> `term_AR_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AR_5_forAll";
    /// `lhs` -> `term_AR_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AR_5_lhs";
    /// `rhs` -> `term_AR_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AR_5_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Phase space definition.
pub mod pd_1 {
    /// `forAll` -> `term_PD_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PD_1_forAll";
    /// `lhs` -> `term_PD_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PD_1_lhs";
    /// `rhs` -> `term_PD_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PD_1_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Phase boundaries occur where g divides 2^n − 1 or g is a power of 2.
pub mod pd_2 {
    /// `forAll` -> `term_PD_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PD_2_forAll";
    /// `lhs` -> `term_PD_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PD_2_lhs";
    /// `rhs` -> `term_PD_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PD_2_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Parity boundary divides R_n into equal halves.
pub mod pd_3 {
    /// `forAll` -> `term_PD_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PD_3_forAll";
    /// `lhs` -> `term_PD_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PD_3_lhs";
    /// `rhs` -> `term_PD_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PD_3_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Resonance lines in the phase diagram.
pub mod pd_4 {
    /// `forAll` -> `term_PD_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PD_4_forAll";
    /// `lhs` -> `term_PD_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PD_4_lhs";
    /// `rhs` -> `term_PD_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PD_4_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Phase count at level n is at most 2^n (typically O(n)).
pub mod pd_5 {
    /// `forAll` -> `term_PD_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PD_5_forAll";
    /// `lhs` -> `term_PD_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PD_5_lhs";
    /// `rhs` -> `term_PD_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PD_5_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Reversible pinning stores prior state in ancilla site.
pub mod rc_1 {
    /// `forAll` -> `term_RC_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RC_1_forAll";
    /// `lhs` -> `term_RC_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RC_1_lhs";
    /// `rhs` -> `term_RC_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RC_1_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Reversible pinning has zero total entropy change.
pub mod rc_2 {
    /// `forAll` -> `term_RC_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RC_2_forAll";
    /// `lhs` -> `term_RC_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RC_2_lhs";
    /// `rhs` -> `term_RC_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RC_2_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Deferred Landauer cost at ancilla erasure.
pub mod rc_3 {
    /// `forAll` -> `term_RC_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RC_3_forAll";
    /// `lhs` -> `term_RC_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RC_3_lhs";
    /// `rhs` -> `term_RC_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RC_3_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Reversible total cost equals irreversible total cost (redistributed).
pub mod rc_4 {
    /// `forAll` -> `term_RC_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RC_4_forAll";
    /// `lhs` -> `term_RC_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RC_4_lhs";
    /// `rhs` -> `term_RC_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RC_4_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Quantum UOR: superposed sites, cost proportional to winning path.
pub mod rc_5 {
    /// `forAll` -> `term_RC_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RC_5_forAll";
    /// `lhs` -> `term_RC_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RC_5_lhs";
    /// `rhs` -> `term_RC_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RC_5_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Ring derivative: ∂_R f(x) = f(succ(x)) - f(x).
pub mod dc_1 {
    /// `forAll` -> `term_DC_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_1_forAll";
    /// `lhs` -> `term_DC_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_1_lhs";
    /// `rhs` -> `term_DC_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Hamming derivative: ∂_H f(x) = f(bnot(x)) - f(x).
pub mod dc_2 {
    /// `forAll` -> `term_DC_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_2_forAll";
    /// `lhs` -> `term_DC_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_2_lhs";
    /// `rhs` -> `term_DC_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_2_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Hamming derivative of identity: ∂_H id(x) = -(2x + 1) mod 2^n.
pub mod dc_3 {
    /// `forAll` -> `term_DC_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_3_forAll";
    /// `lhs` -> `term_DC_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_3_lhs";
    /// `rhs` -> `term_DC_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_3_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Commutator from derivatives: \[neg, bnot\](x) = ∂_R neg(x) - ∂_H neg(x).
pub mod dc_4 {
    /// `forAll` -> `term_DC_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_4_forAll";
    /// `lhs` -> `term_DC_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_4_lhs";
    /// `rhs` -> `term_DC_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Carry dependence: the difference ∂_R f - ∂_H f decomposes into carry contributions.
pub mod dc_5 {
    /// `forAll` -> `term_DC_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_5_forAll";
    /// `lhs` -> `term_DC_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_5_lhs";
    /// `rhs` -> `term_DC_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_5_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Jacobian definition: J_k(x) = ∂_R f_k(x) where f_k = site_k.
pub mod dc_6 {
    /// `forAll` -> `term_DC_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_6_forAll";
    /// `lhs` -> `term_DC_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_6_lhs";
    /// `rhs` -> `term_DC_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_6_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Top-site anomaly: J_{n-1}(x) may differ from lower sites.
pub mod dc_7 {
    /// `forAll` -> `term_DC_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_7_forAll";
    /// `lhs` -> `term_DC_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_7_lhs";
    /// `rhs` -> `term_DC_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_7_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Rank-curvature identity: rank(J(x)) = d_H(x, succ(x)) - 1 for generic x.
pub mod dc_8 {
    /// `forAll` -> `term_DC_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_8_forAll";
    /// `lhs` -> `term_DC_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_8_lhs";
    /// `rhs` -> `term_DC_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_8_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Total curvature from Jacobian: κ(x) = Σ_k J_k(x).
pub mod dc_9 {
    /// `forAll` -> `term_DC_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_9_forAll";
    /// `lhs` -> `term_DC_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_9_lhs";
    /// `rhs` -> `term_DC_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_9_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Curvature-weighted ordering: optimal next constraint maximizes J_k over free sites.
pub mod dc_10 {
    /// `forAll` -> `term_DC_10_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_10_forAll";
    /// `lhs` -> `term_DC_10_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_10_lhs";
    /// `rhs` -> `term_DC_10_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_10_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Curvature equipartition: Σ_{x} J_k(x) ≈ (2^n - 2)/n for each k.
pub mod dc_11 {
    /// `forAll` -> `term_DC_11_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DC_11_forAll";
    /// `lhs` -> `term_DC_11_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DC_11_lhs";
    /// `rhs` -> `term_DC_11_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DC_11_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Constraint nerve: N(C) is the simplicial complex on constraints.
pub mod ha_1 {
    /// `forAll` -> `term_HA_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HA_1_forAll";
    /// `lhs` -> `term_HA_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HA_1_lhs";
    /// `rhs` -> `term_HA_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HA_1_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Stall iff non-trivial homology: resolution stalls ⟺ H_k(N(C)) ≠ 0 for some k > 0.
pub mod ha_2 {
    /// `forAll` -> `term_HA_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HA_2_forAll";
    /// `lhs` -> `term_HA_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HA_2_lhs";
    /// `rhs` -> `term_HA_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HA_2_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Betti-entropy theorem: S_residual ≥ Σ_k β_k × ln 2.
pub mod ha_3 {
    /// `forAll` -> `term_HA_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HA_3_forAll";
    /// `lhs` -> `term_HA_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HA_3_lhs";
    /// `rhs` -> `term_HA_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HA_3_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Euler-Poincaré formula for constraint nerve.
pub mod it_2 {
    /// `forAll` -> `term_IT_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IT_2_forAll";
    /// `lhs` -> `term_IT_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IT_2_lhs";
    /// `rhs` -> `term_IT_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IT_2_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Spectral Euler characteristic.
pub mod it_3 {
    /// `forAll` -> `term_IT_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IT_3_forAll";
    /// `lhs` -> `term_IT_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IT_3_lhs";
    /// `rhs` -> `term_IT_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IT_3_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Spectral gap bounds convergence rate from below.
pub mod it_6 {
    /// `forAll` -> `term_IT_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IT_6_forAll";
    /// `lhs` -> `term_IT_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IT_6_lhs";
    /// `rhs` -> `term_IT_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IT_6_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// UOR index theorem (topological form): total curvature minus Euler characteristic equals residual entropy in bits.
pub mod it_7a {
    /// `forAll` -> `term_IT_7a_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IT_7a_forAll";
    /// `lhs` -> `term_IT_7a_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IT_7a_lhs";
    /// `rhs` -> `term_IT_7a_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IT_7a_rhs";
    /// `verificationDomain`
    pub const VERIFICATION_DOMAIN: &[&str] = &[
        "https://uor.foundation/op/IndexTheoretic",
        "https://uor.foundation/op/Analytical",
        "https://uor.foundation/op/Topological",
    ];
}

/// UOR index theorem (entropy-topology duality).
pub mod it_7b {
    /// `forAll` -> `term_IT_7b_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IT_7b_forAll";
    /// `lhs` -> `term_IT_7b_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IT_7b_lhs";
    /// `rhs` -> `term_IT_7b_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IT_7b_rhs";
    /// `verificationDomain`
    pub const VERIFICATION_DOMAIN: &[&str] = &[
        "https://uor.foundation/op/IndexTheoretic",
        "https://uor.foundation/op/Analytical",
        "https://uor.foundation/op/Topological",
    ];
}

/// UOR index theorem (spectral cost bound): resolution cost ≥ n - χ(N(C)).
pub mod it_7c {
    /// `forAll` -> `term_IT_7c_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IT_7c_forAll";
    /// `lhs` -> `term_IT_7c_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IT_7c_lhs";
    /// `rhs` -> `term_IT_7c_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IT_7c_rhs";
    /// `verificationDomain`
    pub const VERIFICATION_DOMAIN: &[&str] = &[
        "https://uor.foundation/op/IndexTheoretic",
        "https://uor.foundation/op/Analytical",
        "https://uor.foundation/op/Topological",
    ];
}

/// UOR index theorem (completeness criterion): resolution is complete iff χ(N(C)) = n and all Betti numbers vanish.
pub mod it_7d {
    /// `forAll` -> `term_IT_7d_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IT_7d_forAll";
    /// `lhs` -> `term_IT_7d_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IT_7d_lhs";
    /// `rhs` -> `term_IT_7d_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IT_7d_rhs";
    /// `verificationDomain`
    pub const VERIFICATION_DOMAIN: &[&str] = &[
        "https://uor.foundation/op/IndexTheoretic",
        "https://uor.foundation/op/Analytical",
        "https://uor.foundation/op/Topological",
    ];
}

/// Ring → Constraints map: negation transforms a residue constraint.
pub mod phi_1 {
    /// `forAll` -> `term_phi_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_phi_1_forAll";
    /// `lhs` -> `term_phi_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_phi_1_lhs";
    /// `rhs` -> `term_phi_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_phi_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Constraints → Sites map: composition maps to union of site pinnings.
pub mod phi_2 {
    /// `forAll` -> `term_phi_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_phi_2_forAll";
    /// `lhs` -> `term_phi_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_phi_2_lhs";
    /// `rhs` -> `term_phi_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_phi_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Sites → Partition map: a closed site state determines a unique 4-component partition.
pub mod phi_3 {
    /// `forAll` -> `term_phi_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_phi_3_forAll";
    /// `lhs` -> `term_phi_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_phi_3_lhs";
    /// `rhs` -> `term_phi_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_phi_3_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Resolution pipeline: φ₄ = φ₃ ∘ φ₂ ∘ φ₁ is the composite resolution map.
pub mod phi_4 {
    /// `forAll` -> `term_phi_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_phi_4_forAll";
    /// `lhs` -> `term_phi_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_phi_4_lhs";
    /// `rhs` -> `term_phi_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_phi_4_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Operations → Observables map: negation preserves d_R, may change d_H.
pub mod phi_5 {
    /// `forAll` -> `term_phi_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_phi_5_forAll";
    /// `lhs` -> `term_phi_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_phi_5_lhs";
    /// `rhs` -> `term_phi_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_phi_5_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Observables → Refinement map: observables on a state yield a refinement suggestion.
pub mod phi_6 {
    /// `forAll` -> `term_phi_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_phi_6_forAll";
    /// `lhs` -> `term_phi_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_phi_6_lhs";
    /// `rhs` -> `term_phi_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_phi_6_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// ψ_1: Constraints → SimplicialComplex (nerve construction). Maps a set of constraints to its nerve simplicial complex.
pub mod psi_1 {
    /// `forAll` -> `term_psi_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_psi_1_forAll";
    /// `lhs` -> `term_psi_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_psi_1_lhs";
    /// `rhs` -> `term_psi_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_psi_1_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// ψ_2: SimplicialComplex → ChainComplex (chain functor). Maps a simplicial complex to its chain complex.
pub mod psi_2 {
    /// `forAll` -> `term_psi_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_psi_2_forAll";
    /// `lhs` -> `term_psi_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_psi_2_lhs";
    /// `rhs` -> `term_psi_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_psi_2_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// ψ_3: ChainComplex → HomologyGroups (homology functor). Computes homology groups from a chain complex.
pub mod psi_3 {
    /// `forAll` -> `term_psi_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_psi_3_forAll";
    /// `lhs` -> `term_psi_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_psi_3_lhs";
    /// `rhs` -> `term_psi_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_psi_3_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// ψ_5: ChainComplex → CochainComplex (dualization functor). Dualizes a chain complex to obtain a cochain complex.
pub mod psi_5 {
    /// `forAll` -> `term_psi_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_psi_5_forAll";
    /// `lhs` -> `term_psi_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_psi_5_lhs";
    /// `rhs` -> `term_psi_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_psi_5_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// ψ_6: CochainComplex → CohomologyGroups (cohomology functor). Computes cohomology groups from a cochain complex.
pub mod psi_6 {
    /// `forAll` -> `term_psi_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_psi_6_forAll";
    /// `lhs` -> `term_psi_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_psi_6_lhs";
    /// `rhs` -> `term_psi_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_psi_6_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// The dihedral group of order 2^(n+1), generated by neg (ring reflection) and bnot (hypercube reflection). Every element of this group acts as an isometry on the type space 𝒯_n.
pub mod d2n {
    /// `generatedBy`
    pub const GENERATED_BY: &[&str] = &[
        "https://uor.foundation/op/neg",
        "https://uor.foundation/op/bnot",
    ];
    /// `presentation`
    pub const PRESENTATION: &str = "⟨r, s | r^{2^n} = s² = e, srs = r⁻¹⟩";
}

/// The Surface Symmetry Theorem: the composite P∘Π∘G is a well-typed morphism iff G and P share the same state:Frame F. When the shared-frame condition holds, the output lands in the type-equivalent neighbourhood of the source symbol.
pub mod surface_symmetry {
    /// `forAll` -> `term_surfaceSymmetry_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_surfaceSymmetry_forAll";
    /// `lhs` -> `term_surfaceSymmetry_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_surfaceSymmetry_lhs";
    /// `rhs` -> `term_surfaceSymmetry_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_surfaceSymmetry_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Completeness implies O(1) resolution: a CompleteType T satisfies ∀ x ∈ R_n, resolution(x, T) terminates in O(1).
pub mod cc_1 {
    /// `forAll` -> `term_CC_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CC_1_forAll";
    /// `lhs` -> `term_CC_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CC_1_lhs";
    /// `rhs` -> `term_CC_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CC_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Completeness is monotone: if T ⊆ T' (T' has more constraints), then completeness(T) implies completeness(T').
pub mod cc_2 {
    /// `forAll` -> `term_CC_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CC_2_forAll";
    /// `lhs` -> `term_CC_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CC_2_lhs";
    /// `rhs` -> `term_CC_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CC_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Witness composition: concat(W₁, W₂) is a valid audit trail iff W₁.sitesClosed + W₂.sitesClosed = n.
pub mod cc_3 {
    /// `forAll` -> `term_CC_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CC_3_forAll";
    /// `lhs` -> `term_CC_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CC_3_lhs";
    /// `rhs` -> `term_CC_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CC_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The CompletenessResolver is the unique fixed point of the ψ-pipeline applied to a CompletenessCandidate.
pub mod cc_4 {
    /// `forAll` -> `term_CC_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CC_4_forAll";
    /// `lhs` -> `term_CC_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CC_4_lhs";
    /// `rhs` -> `term_CC_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CC_4_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// CompletenessCertificate soundness: cert.verified = true implies χ(N(C)) = n and for all k: β_k = 0.
pub mod cc_5 {
    /// `forAll` -> `term_CC_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CC_5_forAll";
    /// `lhs` -> `term_CC_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CC_5_lhs";
    /// `rhs` -> `term_CC_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CC_5_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// neg(bnot(x)) = succ(x) holds in Z/(2ⁿ)Z for all n ≥ 1. Universal form of the Critical Identity across all quantum levels.
pub mod ql_1 {
    /// `forAll` -> `term_QL_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QL_1_forAll";
    /// `lhs` -> `term_QL_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QL_1_lhs";
    /// `rhs` -> `term_QL_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QL_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The dihedral group D_{2ⁿ} generated by neg and bnot has order 2ⁿ⁺¹ for all n ≥ 1.
pub mod ql_2 {
    /// `forAll` -> `term_QL_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QL_2_forAll";
    /// `lhs` -> `term_QL_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QL_2_lhs";
    /// `rhs` -> `term_QL_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QL_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The reduction distribution P(j) = 2^{-j} is the Boltzmann distribution at β* = ln 2 for all n ≥ 1.
pub mod ql_3 {
    /// `forAll` -> `term_QL_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QL_3_forAll";
    /// `lhs` -> `term_QL_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QL_3_lhs";
    /// `rhs` -> `term_QL_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QL_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// The site budget of a PrimitiveType at quantum level n is exactly n (one site per bit).
pub mod ql_4 {
    /// `forAll` -> `term_QL_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QL_4_forAll";
    /// `lhs` -> `term_QL_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QL_4_lhs";
    /// `rhs` -> `term_QL_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QL_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Resolution complexity for a CompleteType is O(1) for all n ≥ 1.
pub mod ql_5 {
    /// `forAll` -> `term_QL_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QL_5_forAll";
    /// `lhs` -> `term_QL_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QL_5_lhs";
    /// `rhs` -> `term_QL_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QL_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Content addressing is a bijection for all n ≥ 1 (AD_1/AD_2 universality).
pub mod ql_6 {
    /// `forAll` -> `term_QL_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QL_6_forAll";
    /// `lhs` -> `term_QL_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QL_6_lhs";
    /// `rhs` -> `term_QL_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QL_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The ψ-pipeline produces a valid ChainComplex for any ConstrainedType at any quantum level n ≥ 1.
pub mod ql_7 {
    /// `forAll` -> `term_QL_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QL_7_forAll";
    /// `lhs` -> `term_QL_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QL_7_lhs";
    /// `rhs` -> `term_QL_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QL_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Binding monotonicity: freeRank(B_{i+1}) ≤ freeRank(B_i) for all i in a Session.
pub mod gr_1 {
    /// `forAll` -> `term_GR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_1_forAll";
    /// `lhs` -> `term_GR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_1_lhs";
    /// `rhs` -> `term_GR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Binding soundness: a Binding b is sound iff b.datum resolves under b.constraint in O(1).
pub mod gr_2 {
    /// `forAll` -> `term_GR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_2_forAll";
    /// `lhs` -> `term_GR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_2_lhs";
    /// `rhs` -> `term_GR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Session convergence: a Session S converges iff there exists i such that freeRank(B_i) = 0.
pub mod gr_3 {
    /// `forAll` -> `term_GR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_3_forAll";
    /// `lhs` -> `term_GR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_3_lhs";
    /// `rhs` -> `term_GR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Context reset isolation: bindings in C_fresh are independent of bindings in C_prior after a SessionBoundary.
pub mod gr_4 {
    /// `forAll` -> `term_GR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_4_forAll";
    /// `lhs` -> `term_GR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_4_lhs";
    /// `rhs` -> `term_GR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Contradiction detection: ContradictionBoundary fires iff there exist bindings b, b' with the same address, different datum, under the same constraint.
pub mod gr_5 {
    /// `forAll` -> `term_GR_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_5_forAll";
    /// `lhs` -> `term_GR_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_5_lhs";
    /// `rhs` -> `term_GR_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_5_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Nerve realisability: for any target (χ*, β₀* = 1, β_k* = 0 for k ≥ 1) with χ* ≤ n, there exists a ConstrainedType T over R_n whose constraint nerve realises the target.
pub mod ts_1 {
    /// `forAll` -> `term_TS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_1_forAll";
    /// `lhs` -> `term_TS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_1_lhs";
    /// `rhs` -> `term_TS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Minimal basis bound: for the IT_7d target (χ* = n, all β* = 0), the MinimalConstraintBasis has size exactly n (one constraint per site position). No redundant constraints exist in the minimal basis.
pub mod ts_2 {
    /// `forAll` -> `term_TS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_2_forAll";
    /// `lhs` -> `term_TS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_2_lhs";
    /// `rhs` -> `term_TS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_2_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Synthesis monotonicity: adding a constraint to a synthesis candidate never decreases the Euler characteristic of the resulting nerve (χ is monotone non-decreasing under constraint addition).
pub mod ts_3 {
    /// `forAll` -> `term_TS_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_3_forAll";
    /// `lhs` -> `term_TS_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_3_lhs";
    /// `rhs` -> `term_TS_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_3_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Synthesis convergence: the TypeSynthesisResolver terminates for any realisable target in at most n constraint additions (for n-site types).
pub mod ts_4 {
    /// `forAll` -> `term_TS_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_4_forAll";
    /// `lhs` -> `term_TS_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_4_lhs";
    /// `rhs` -> `term_TS_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_4_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Synthesis–certification duality: a SynthesizedType T achieves the IT_7d target if and only if the CompletenessResolver certifies T as a CompleteType. The forward ψ-pipeline and the inverse TypeSynthesisResolver are dual computations.
pub mod ts_5 {
    /// `forAll` -> `term_TS_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_5_forAll";
    /// `lhs` -> `term_TS_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_5_lhs";
    /// `rhs` -> `term_TS_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_5_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Jacobian-guided synthesis efficiency: using the Jacobian (DC_10) to select the next constraint reduces the expected number of synthesis steps from O(n²) (uninformed) to O(n log n) (Jacobian-guided).
pub mod ts_6 {
    /// `forAll` -> `term_TS_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_6_forAll";
    /// `lhs` -> `term_TS_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_6_lhs";
    /// `rhs` -> `term_TS_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_6_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Unreachable signatures: a Betti profile with β₀ = 0 is unreachable by any non-empty ConstrainedType — the nerve of a non-empty constraint set is always connected (β₀ ≥ 1).
pub mod ts_7 {
    /// `forAll` -> `term_TS_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_7_forAll";
    /// `lhs` -> `term_TS_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_7_lhs";
    /// `rhs` -> `term_TS_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_7_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Lift unobstructedness criterion: WittLift T' is a CompleteType iff the spectral sequence E_r^{p,q} collapses at E_2 (d_2 = 0 and all higher differentials zero).
pub mod wls_1 {
    /// `forAll` -> `term_WLS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WLS_1_forAll";
    /// `lhs` -> `term_WLS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WLS_1_lhs";
    /// `rhs` -> `term_WLS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WLS_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Obstruction localisation: a non-trivial LiftObstruction is localised to a specific site at bit position n+1. The obstruction class lives in H²(N(C(T))) and is killed by adding one constraint involving the new site.
pub mod wls_2 {
    /// `forAll` -> `term_WLS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WLS_2_forAll";
    /// `lhs` -> `term_WLS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WLS_2_lhs";
    /// `rhs` -> `term_WLS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WLS_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Monotone lifting for trivially obstructed types: if T is a CompleteType at Q_n and its constraint set is closed under the Q_{n+1} extension map, then T' is a CompleteType at Q_{n+1} with basisSize(T') = basisSize(T) + 1.
pub mod wls_3 {
    /// `forAll` -> `term_WLS_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WLS_3_forAll";
    /// `lhs` -> `term_WLS_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WLS_3_lhs";
    /// `rhs` -> `term_WLS_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WLS_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Spectral sequence convergence bound: for constraint configurations of homological depth d (H_k(N(C(T))) = 0 for k > d), the spectral sequence converges by page E_{d+2}.
pub mod wls_4 {
    /// `forAll` -> `term_WLS_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WLS_4_forAll";
    /// `lhs` -> `term_WLS_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WLS_4_lhs";
    /// `rhs` -> `term_WLS_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WLS_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Universal identity preservation: every op:universallyValid identity holds in ℤ/(2^{n+1})ℤ with the lifted constraint set. The lift does not invalidate any certified universal identity.
pub mod wls_5 {
    /// `forAll` -> `term_WLS_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WLS_5_forAll";
    /// `lhs` -> `term_WLS_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WLS_5_lhs";
    /// `rhs` -> `term_WLS_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WLS_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// ψ-pipeline universality for quantum lifts: the ψ-pipeline produces a valid ChainComplex for any WittLift T' — the chain complex of T' restricts to the chain complex of T on the base nerve, and the extension is well-formed by construction.
pub mod wls_6 {
    /// `forAll` -> `term_WLS_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WLS_6_forAll";
    /// `lhs` -> `term_WLS_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WLS_6_lhs";
    /// `rhs` -> `term_WLS_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WLS_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Holonomy group containment: HolonomyGroup(T) ≤ D_{2^n} for all ConstrainedTypes T over R_n. The holonomy group is always a subgroup of the full dihedral group.
pub mod mn_1 {
    /// `forAll` -> `term_MN_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MN_1_forAll";
    /// `lhs` -> `term_MN_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MN_1_lhs";
    /// `rhs` -> `term_MN_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MN_1_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Additive flatness (extends OB_H1): if all constraints in T are additive (ResidueConstraint or DepthConstraint type), then HolonomyGroup(T) = {id} — T is a FlatType.
pub mod mn_2 {
    /// `forAll` -> `term_MN_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MN_2_forAll";
    /// `lhs` -> `term_MN_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MN_2_lhs";
    /// `rhs` -> `term_MN_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MN_2_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Dihedral generation: if T contains both a neg-related and a bnot-related constraint in a common closed path, then HolonomyGroup(T) = D_{2^n} — T has full dihedral holonomy.
pub mod mn_3 {
    /// `forAll` -> `term_MN_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MN_3_forAll";
    /// `lhs` -> `term_MN_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MN_3_lhs";
    /// `rhs` -> `term_MN_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MN_3_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Holonomy-Betti implication: HolonomyGroup(T) ≠ {id} ⟹ β₁(N(C(T))) ≥ 1. Non-trivial monodromy requires a topological loop. (Converse is false: β₁ ≥ 1 does not imply non-trivial holonomy.)
pub mod mn_4 {
    /// `forAll` -> `term_MN_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MN_4_forAll";
    /// `lhs` -> `term_MN_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MN_4_lhs";
    /// `rhs` -> `term_MN_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MN_4_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// CompleteType holonomy: a CompleteType (IT_7d: χ = n, all β = 0) has trivial holonomy. IT_7d implies FlatType because IT_7d requires β₁ = 0, which by MN_4 implies trivial monodromy.
pub mod mn_5 {
    /// `forAll` -> `term_MN_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MN_5_forAll";
    /// `lhs` -> `term_MN_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MN_5_lhs";
    /// `rhs` -> `term_MN_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MN_5_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Monodromy composition: if p₁ and p₂ are closed constraint paths, then monodromy(p₁ · p₂) = monodromy(p₁) · monodromy(p₂) in D_{2^n} (group homomorphism from loops to dihedral elements).
pub mod mn_6 {
    /// `forAll` -> `term_MN_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MN_6_forAll";
    /// `lhs` -> `term_MN_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MN_6_lhs";
    /// `rhs` -> `term_MN_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MN_6_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// TwistedType obstruction class: the monodromy of a TwistedType contributes a non-zero class to H²(N(C(T')); ℤ/2ℤ) where T' is any WittLift of T. TwistedTypes always have non-trivial lift obstructions.
pub mod mn_7 {
    /// `forAll` -> `term_MN_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MN_7_forAll";
    /// `lhs` -> `term_MN_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MN_7_lhs";
    /// `rhs` -> `term_MN_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MN_7_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Product type site additivity: siteBudget(A × B) = siteBudget(A) + siteBudget(B).
pub mod pt_1 {
    /// `forAll` -> `term_PT_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PT_1_forAll";
    /// `lhs` -> `term_PT_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PT_1_lhs";
    /// `rhs` -> `term_PT_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PT_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Product type partition product: partition(A × B) = partition(A) ⊗ partition(B). v0.2.2 T1.3: grounds cert:PartitionCertificate — every PartitionCertificate attests the PartitionComponent classification (Irreducible / Reducible / Units / Exterior) derived from this partition-map identity.
pub mod pt_2 {
    /// `forAll` -> `term_PT_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PT_2_forAll";
    /// `lhs` -> `term_PT_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PT_2_lhs";
    /// `rhs` -> `term_PT_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PT_2_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Product type Euler additivity: χ(N(C(A × B))) = χ(N(C(A))) + χ(N(C(B))).
pub mod pt_3 {
    /// `forAll` -> `term_PT_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PT_3_forAll";
    /// `lhs` -> `term_PT_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PT_3_lhs";
    /// `rhs` -> `term_PT_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PT_3_rhs";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Product type entropy additivity: S(A × B) = S(A) + S(B).
pub mod pt_4 {
    /// `forAll` -> `term_PT_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PT_4_forAll";
    /// `lhs` -> `term_PT_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PT_4_lhs";
    /// `rhs` -> `term_PT_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PT_4_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Sum type site budget: siteBudget(A + B) = max(siteBudget(A), siteBudget(B)).
pub mod st_1 {
    /// `forAll` -> `term_ST_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_1_forAll";
    /// `lhs` -> `term_ST_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_1_lhs";
    /// `rhs` -> `term_ST_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Sum type entropy: S(A + B) = ln 2 + max(S(A), S(B)).
pub mod st_2 {
    /// `forAll` -> `term_ST_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_2_forAll";
    /// `lhs` -> `term_ST_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_2_lhs";
    /// `rhs` -> `term_ST_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_2_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Context temperature: T_ctx(C) = freeRank(C) × ln 2 / n.
pub mod gs_1 {
    /// `forAll` -> `term_GS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GS_1_forAll";
    /// `lhs` -> `term_GS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GS_1_lhs";
    /// `rhs` -> `term_GS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GS_1_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Grounding degree: σ(C) = (n − freeRank(C)) / n.
pub mod gs_2 {
    /// `forAll` -> `term_GS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GS_2_forAll";
    /// `lhs` -> `term_GS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GS_2_lhs";
    /// `rhs` -> `term_GS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GS_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Grounding monotonicity: σ(B_{i+1}) ≥ σ(B_i) for all i in a Session.
pub mod gs_3 {
    /// `forAll` -> `term_GS_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GS_3_forAll";
    /// `lhs` -> `term_GS_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GS_3_lhs";
    /// `rhs` -> `term_GS_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GS_3_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Ground state equivalence: σ(C) = 1 ↔ freeRank(C) = 0 ↔ S(C) = 0 ↔ T_ctx(C) = 0.
pub mod gs_4 {
    /// `forAll` -> `term_GS_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GS_4_forAll";
    /// `lhs` -> `term_GS_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GS_4_lhs";
    /// `rhs` -> `term_GS_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GS_4_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// O(1) resolution guarantee: freeRank(C) = 0 ∧ q.address ∈ bindings(C) → stepCount(q, C) = 0.
pub mod gs_5 {
    /// `forAll` -> `term_GS_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GS_5_forAll";
    /// `lhs` -> `term_GS_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GS_5_lhs";
    /// `rhs` -> `term_GS_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GS_5_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Pre-reduction of effective budget: effectiveBudget(q, C) = max(0, siteBudget(q.type) − |pinnedSites(C) ∩ q.siteSet|).
pub mod gs_6 {
    /// `forAll` -> `term_GS_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GS_6_forAll";
    /// `lhs` -> `term_GS_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GS_6_lhs";
    /// `rhs` -> `term_GS_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GS_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Thermodynamic cooling cost: Cost_saturation(C) = n × k_B T × ln 2.
pub mod gs_7 {
    /// `forAll` -> `term_GS_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GS_7_forAll";
    /// `lhs` -> `term_GS_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GS_7_lhs";
    /// `rhs` -> `term_GS_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GS_7_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Connectivity lower bound: β₀(N(C)) ≥ 1 for all non-empty C.
pub mod ms_1 {
    /// `forAll` -> `term_MS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MS_1_forAll";
    /// `lhs` -> `term_MS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MS_1_lhs";
    /// `rhs` -> `term_MS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MS_1_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Euler capacity ceiling: χ(N(C)) ≤ n for all C at quantum level n.
pub mod ms_2 {
    /// `forAll` -> `term_MS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MS_2_forAll";
    /// `lhs` -> `term_MS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MS_2_lhs";
    /// `rhs` -> `term_MS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MS_2_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Betti monotonicity under addition: χ(N(C + c)) ≥ χ(N(C)) for any constraint c added to C.
pub mod ms_3 {
    /// `forAll` -> `term_MS_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MS_3_forAll";
    /// `lhs` -> `term_MS_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MS_3_lhs";
    /// `rhs` -> `term_MS_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MS_3_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Level-relative achievability: a signature achievable at quantum level n remains achievable at level n+1.
pub mod ms_4 {
    /// `forAll` -> `term_MS_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MS_4_forAll";
    /// `lhs` -> `term_MS_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MS_4_lhs";
    /// `rhs` -> `term_MS_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MS_4_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Empirical completeness convergence: verified SynthesisSignature individuals converge to the exact morphospace boundary.
pub mod ms_5 {
    /// `forAll` -> `term_MS_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MS_5_forAll";
    /// `lhs` -> `term_MS_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MS_5_lhs";
    /// `rhs` -> `term_MS_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MS_5_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Geodesic condition: a ComputationTrace is a geodesic iff its steps are AR_1-ordered and each step selects the constraint maximising J_k over free sites (DC_10).
pub mod gd_1 {
    /// `forAll` -> `term_GD_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GD_1_forAll";
    /// `lhs` -> `term_GD_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GD_1_lhs";
    /// `rhs` -> `term_GD_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GD_1_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Geodesic entropy bound: ΔS_step(i) = ln 2 for every step i of a geodesic trace.
pub mod gd_2 {
    /// `forAll` -> `term_GD_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GD_2_forAll";
    /// `lhs` -> `term_GD_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GD_2_lhs";
    /// `rhs` -> `term_GD_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GD_2_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Total geodesic cost: Cost_geodesic(T) = freeRank_initial × k_B T ln 2 = TH_4.
pub mod gd_3 {
    /// `forAll` -> `term_GD_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GD_3_forAll";
    /// `lhs` -> `term_GD_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GD_3_lhs";
    /// `rhs` -> `term_GD_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GD_3_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Geodesic uniqueness up to step-order equivalence: all geodesics for the same ConstrainedType share stepCount and constraint set.
pub mod gd_4 {
    /// `forAll` -> `term_GD_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GD_4_forAll";
    /// `lhs` -> `term_GD_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GD_4_lhs";
    /// `rhs` -> `term_GD_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GD_4_rhs";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Subgeodesic detectability: a trace is sub-geodesic iff ∃ step i where J_k(step_i) < max_{free sites} J_k(state_i).
pub mod gd_5 {
    /// `forAll` -> `term_GD_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GD_5_forAll";
    /// `lhs` -> `term_GD_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GD_5_lhs";
    /// `rhs` -> `term_GD_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GD_5_rhs";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Von Neumann–Landauer bridge: S_vonNeumann(ψ) = Cost_Landauer(collapse(ψ)).
pub mod qm_1 {
    /// `forAll` -> `term_QM_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QM_1_forAll";
    /// `lhs` -> `term_QM_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QM_1_lhs";
    /// `rhs` -> `term_QM_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QM_1_rhs";
    /// `verificationDomain` -> `QuantumThermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/QuantumThermodynamic";
}

/// Measurement as site topology change: projective collapse on a SuperposedSiteState is topologically equivalent to applying a ResidueConstraint that pins the collapsed site.
pub mod qm_2 {
    /// `forAll` -> `term_QM_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QM_2_forAll";
    /// `lhs` -> `term_QM_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QM_2_lhs";
    /// `rhs` -> `term_QM_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QM_2_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Superposition entropy bound: 0 ≤ S_vN(ψ) ≤ ln 2 for any single-site SuperposedSiteState.
pub mod qm_3 {
    /// `forAll` -> `term_QM_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QM_3_forAll";
    /// `lhs` -> `term_QM_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QM_3_lhs";
    /// `rhs` -> `term_QM_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QM_3_rhs";
    /// `verificationDomain` -> `QuantumThermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/QuantumThermodynamic";
}

/// Collapse idempotence: collapse(collapse(ψ)) = collapse(ψ). Measurement on an already-collapsed state is a no-op.
pub mod qm_4 {
    /// `forAll` -> `term_QM_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QM_4_forAll";
    /// `lhs` -> `term_QM_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QM_4_lhs";
    /// `rhs` -> `term_QM_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QM_4_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Amplitude normalization (Born rule): the sum of squared amplitudes equals 1 for any well-formed SuperposedSiteState.
pub mod qm_5 {
    /// `forAll` -> `term_QM_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QM_5_forAll";
    /// `lhs` -> `term_QM_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QM_5_lhs";
    /// `rhs` -> `term_QM_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QM_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `QuantumThermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/QuantumThermodynamic";
}

/// Amplitude renormalization: a SuperposedSiteState can always be normalized to satisfy QM_5.
pub mod rc_6 {
    /// `forAll` -> `term_RC_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RC_6_forAll";
    /// `lhs` -> `term_RC_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RC_6_lhs";
    /// `rhs` -> `term_RC_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RC_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `SuperpositionDomain`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/SuperpositionDomain";
}

/// Partition exhaustiveness: the four component cardinalities sum to the ring size.
pub mod fpm_8 {
    /// `forAll` -> `term_FPM_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_8_forAll";
    /// `lhs` -> `term_FPM_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_8_lhs";
    /// `rhs` -> `term_FPM_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Enumerative`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Enumerative";
}

/// Exterior membership criterion: x is exterior iff x is not in the carrier of T.
pub mod fpm_9 {
    /// `forAll` -> `term_FPM_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FPM_9_forAll";
    /// `lhs` -> `term_FPM_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FPM_9_lhs";
    /// `rhs` -> `term_FPM_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FPM_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Holonomy classification covering: every ConstrainedType with a computed holonomy group is either flat or twisted, not both.
pub mod mn_8 {
    /// `forAll` -> `term_MN_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MN_8_forAll";
    /// `lhs` -> `term_MN_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MN_8_lhs";
    /// `rhs` -> `term_MN_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MN_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Witt level chain inverse: wittLevelPredecessor is the left inverse of nextWittLevel.
pub mod ql_8 {
    /// `forAll` -> `term_QL_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QL_8_forAll";
    /// `lhs` -> `term_QL_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QL_8_lhs";
    /// `rhs` -> `term_QL_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QL_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Dihedral composition rule: (rᵃ sᵖ)(rᵇ sᵠ) = r^(a + (-1)ᵖ b mod 2ⁿ) s^(p xor q).
pub mod d_7 {
    /// `forAll` -> `term_D_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_D_7_forAll";
    /// `lhs` -> `term_D_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_D_7_lhs";
    /// `rhs` -> `term_D_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_D_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Classical embedding: superposition resolution of a classical (non-superposed) datum reduces to classical resolution.
pub mod sp_1 {
    /// `forAll` -> `term_SP_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SP_1_forAll";
    /// `lhs` -> `term_SP_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SP_1_lhs";
    /// `rhs` -> `term_SP_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SP_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `SuperpositionDomain`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/SuperpositionDomain";
}

/// Collapse–resolve commutativity: collapsing then resolving classically equals resolving in superposition then collapsing.
pub mod sp_2 {
    /// `forAll` -> `term_SP_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SP_2_forAll";
    /// `lhs` -> `term_SP_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SP_2_lhs";
    /// `rhs` -> `term_SP_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SP_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `QuantumThermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/QuantumThermodynamic";
}

/// Amplitude preservation: the SuperpositionResolver preserves the normalized amplitude vector during ψ-pipeline traversal.
pub mod sp_3 {
    /// `forAll` -> `term_SP_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SP_3_forAll";
    /// `lhs` -> `term_SP_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SP_3_lhs";
    /// `rhs` -> `term_SP_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SP_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `SuperpositionDomain`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/SuperpositionDomain";
}

/// Born rule outcome probability: the probability of collapsing to site k equals the squared amplitude of that site.
pub mod sp_4 {
    /// `forAll` -> `term_SP_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SP_4_forAll";
    /// `lhs` -> `term_SP_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SP_4_lhs";
    /// `rhs` -> `term_SP_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SP_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `QuantumThermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/QuantumThermodynamic";
}

/// Product type partition tensor: the partition of a product type is the tensor product of the component partitions.
pub mod pt_2a {
    /// `forAll` -> `term_PT_2a_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PT_2a_forAll";
    /// `lhs` -> `term_PT_2a_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PT_2a_lhs";
    /// `rhs` -> `term_PT_2a_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PT_2a_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Sum type partition coproduct: the partition of a sum type is the coproduct of the variant partitions.
pub mod pt_2b {
    /// `forAll` -> `term_PT_2b_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PT_2b_forAll";
    /// `lhs` -> `term_PT_2b_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PT_2b_lhs";
    /// `rhs` -> `term_PT_2b_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PT_2b_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Geodesic predicate decomposition: a trace is geodesic iff it is both AR_1-ordered and DC_10-selected.
pub mod gd_6 {
    /// `forAll` -> `term_GD_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GD_6_forAll";
    /// `lhs` -> `term_GD_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GD_6_lhs";
    /// `rhs` -> `term_GD_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GD_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// LiftChain(Q_j, Q_k) is valid CompleteType tower iff every chainStep WittLift has trivial or resolved LiftObstruction.
pub mod wt_1 {
    /// `forAll` -> `term_WT_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_1_forAll";
    /// `lhs` -> `term_WT_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_1_lhs";
    /// `rhs` -> `term_WT_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Obstruction count bound: the number of non-trivial LiftObstructions in a chain is at most the chain length.
pub mod wt_2 {
    /// `forAll` -> `term_WT_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_2_forAll";
    /// `lhs` -> `term_WT_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_2_lhs";
    /// `rhs` -> `term_WT_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Resolved basis size formula: the basis size at Q_k equals basisSize(Q_j) + chainLength + obstructionResolutionCost.
pub mod wt_3 {
    /// `forAll` -> `term_WT_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_3_forAll";
    /// `lhs` -> `term_WT_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_3_lhs";
    /// `rhs` -> `term_WT_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Flat tower characterization: isFlat(chain) iff obstructionCount = 0 iff HolonomyGroup trivial at every step.
pub mod wt_4 {
    /// `forAll` -> `term_WT_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_4_forAll";
    /// `lhs` -> `term_WT_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_4_lhs";
    /// `rhs` -> `term_WT_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// LiftChainCertificate existence: a CompleteType at Q_k satisfies IT_7d with a witness chain.
pub mod wt_5 {
    /// `forAll` -> `term_WT_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_5_forAll";
    /// `lhs` -> `term_WT_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_5_lhs";
    /// `rhs` -> `term_WT_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Single-step reduction: QT_3 with chainLength=1 and cost=0 reduces to QLS_3.
pub mod wt_6 {
    /// `forAll` -> `term_WT_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_6_forAll";
    /// `lhs` -> `term_WT_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_6_lhs";
    /// `rhs` -> `term_WT_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Flat chain basis size: for flat chains, resolvedBasisSize(Q_k) = basisSize(Q_j) + (k - j).
pub mod wt_7 {
    /// `forAll` -> `term_WT_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_7_forAll";
    /// `lhs` -> `term_WT_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_7_lhs";
    /// `rhs` -> `term_WT_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Carry-constraint site-pinning map: pinsSites(CarryConstraint(p)) equals the set of bit positions where p has a 1 plus the first-zero stopping position.
pub mod cc_pins {
    /// `forAll` -> `term_CC_PINS_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CC_PINS_forAll";
    /// `lhs` -> `term_CC_PINS_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CC_PINS_lhs";
    /// `rhs` -> `term_CC_PINS_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CC_PINS_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry-constraint cost-to-site count: the number of sites pinned by a CarryConstraint equals popcount plus one for the stopping position.
pub mod cc_cost_site {
    /// `forAll` -> `term_CC_COST_SITE_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CC_COST_SITE_forAll";
    /// `lhs` -> `term_CC_COST_SITE_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CC_COST_SITE_lhs";
    /// `rhs` -> `term_CC_COST_SITE_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CC_COST_SITE_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Enumerative`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Enumerative";
}

/// CRT joint satisfiability: two ResidueConstraints are jointly satisfiable iff the gcd of their moduli divides the difference of their residues.
pub mod jsat_rr {
    /// `forAll` -> `term_jsat_RR_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_jsat_RR_forAll";
    /// `lhs` -> `term_jsat_RR_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_jsat_RR_lhs";
    /// `rhs` -> `term_jsat_RR_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_jsat_RR_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry-residue joint satisfiability: a CarryConstraint and ResidueConstraint are jointly satisfiable iff the carry-pinned sites are compatible with the residue class.
pub mod jsat_cr {
    /// `forAll` -> `term_jsat_CR_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_jsat_CR_forAll";
    /// `lhs` -> `term_jsat_CR_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_jsat_CR_lhs";
    /// `rhs` -> `term_jsat_CR_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_jsat_CR_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry-carry joint satisfiability: two CarryConstraints are jointly satisfiable iff their bit-patterns have no conflicting positions.
pub mod jsat_cc {
    /// `forAll` -> `term_jsat_CC_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_jsat_CC_forAll";
    /// `lhs` -> `term_jsat_CC_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_jsat_CC_lhs";
    /// `rhs` -> `term_jsat_CC_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_jsat_CC_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Enumerative`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Enumerative";
}

/// Dihedral inverse formula: the inverse of r^a s^p in D_(2^n) is r^(-(−1)^p a mod 2^n) s^p.
pub mod d_8 {
    /// `forAll` -> `term_D_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_D_8_forAll";
    /// `lhs` -> `term_D_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_D_8_lhs";
    /// `rhs` -> `term_D_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_D_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Dihedral reflection order: every reflection element r^k s^1 in D_(2^n) has order 2.
pub mod d_9 {
    /// `forAll` -> `term_D_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_D_9_forAll";
    /// `lhs` -> `term_D_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_D_9_lhs";
    /// `rhs` -> `term_D_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_D_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Monotone carrier characterization: a ConstrainedType has an upward-closed carrier iff every ResidueConstraint has residue = modulus - 1 and no CarryConstraint or DepthConstraint appears.
pub mod exp_1 {
    /// `forAll` -> `term_EXP_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EXP_1_forAll";
    /// `lhs` -> `term_EXP_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EXP_1_lhs";
    /// `rhs` -> `term_EXP_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EXP_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Monotone constraint count: the number of expressible monotone ConstrainedTypes at quantum level Q_n is 2^n, corresponding to the principal filter count.
pub mod exp_2 {
    /// `forAll` -> `term_EXP_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EXP_2_forAll";
    /// `lhs` -> `term_EXP_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EXP_2_lhs";
    /// `rhs` -> `term_EXP_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EXP_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Enumerative`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Enumerative";
}

/// SumType carrier semantics: the carrier of a SumType is the coproduct (disjoint union) of component carriers, not the set-theoretic union.
pub mod exp_3 {
    /// `forAll` -> `term_EXP_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EXP_3_forAll";
    /// `lhs` -> `term_EXP_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EXP_3_lhs";
    /// `rhs` -> `term_EXP_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EXP_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// SumType Euler characteristic additivity: for a SumType with topologically disjoint component nerves, the Euler characteristic is additive.
pub mod st_3 {
    /// `forAll` -> `term_ST_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_3_forAll";
    /// `lhs` -> `term_ST_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_3_lhs";
    /// `rhs` -> `term_ST_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// SumType Betti number additivity: for disjoint component nerves, all Betti numbers are additive.
pub mod st_4 {
    /// `forAll` -> `term_ST_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_4_forAll";
    /// `lhs` -> `term_ST_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_4_lhs";
    /// `rhs` -> `term_ST_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// SumType completeness transfer: a SumType A+B is CompleteType iff both A and B are CompleteType and they have equal quantum levels.
pub mod st_5 {
    /// `forAll` -> `term_ST_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_5_forAll";
    /// `lhs` -> `term_ST_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_5_lhs";
    /// `rhs` -> `term_ST_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// SumType tag site unique existence: every PartitionCoproduct A + B has exactly one tag site, logically distinct from every data site of A and B, carrying the ln 2 entropy quantum of ST_2.
pub mod st_6 {
    /// `forAll` -> `term_ST_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_6_forAll";
    /// `lhs` -> `term_ST_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_6_lhs";
    /// `rhs` -> `term_ST_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// SumType variant tagging: the constraints of a PartitionCoproduct decompose into the operands' constraints plus one tag-pinning constraint per variant (tag = 0 for the left variant, tag = 1 for the right).
pub mod st_7 {
    /// `forAll` -> `term_ST_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_7_forAll";
    /// `lhs` -> `term_ST_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_7_lhs";
    /// `rhs` -> `term_ST_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_7_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// SumType variant nerve disjointness bridge: a PartitionCoproduct constructed via ST_6 + ST_7 + the foundation layout convention produces topologically disjoint component nerves. Bridges the existing conditional ST_3 and ST_4 to PartitionCoproduct constructions concretely.
pub mod st_8 {
    /// `forAll` -> `term_ST_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_8_forAll";
    /// `lhs` -> `term_ST_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_8_lhs";
    /// `rhs` -> `term_ST_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_8_rhs";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// SumType Euler corollary for PartitionCoproduct constructions: combining ST_8's disjointness guarantee with the universal ST_3 yields Euler additivity for any A + B assembled via the PartitionCoproduct construction.
pub mod st_9 {
    /// `forAll` -> `term_ST_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_9_forAll";
    /// `lhs` -> `term_ST_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_9_lhs";
    /// `rhs` -> `term_ST_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_9_rhs";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// SumType Betti corollary for PartitionCoproduct constructions: combining ST_8's disjointness guarantee with the universal ST_4 yields Betti additivity at every dimension for any A + B assembled via the PartitionCoproduct construction.
pub mod st_10 {
    /// `forAll` -> `term_ST_10_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ST_10_forAll";
    /// `lhs` -> `term_ST_10_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ST_10_lhs";
    /// `rhs` -> `term_ST_10_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ST_10_rhs";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Cartesian partition product site additivity: siteBudget(A ⊠ B) = siteBudget(A) + siteBudget(B). UOR sites are bit widths; |A ⊠ B| = 2^{n_A} · 2^{n_B} = 2^{n_A + n_B}, so sites add even though cardinalities multiply.
pub mod cpt_1 {
    /// `forAll` -> `term_CPT_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CPT_1_forAll";
    /// `lhs` -> `term_CPT_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CPT_1_lhs";
    /// `rhs` -> `term_CPT_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CPT_1_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Cartesian partition product partition map: Π(A ⊠ B) = CartesianPartitionProduct(Π(A), Π(B)).
pub mod cpt_2a {
    /// `forAll` -> `term_CPT_2a_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CPT_2a_forAll";
    /// `lhs` -> `term_CPT_2a_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CPT_2a_lhs";
    /// `rhs` -> `term_CPT_2a_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CPT_2a_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Cartesian partition product Euler multiplicativity: χ(N(C(A ⊠ B))) = χ(N(C(A))) · χ(N(C(B))). Distinguishes CartesianPartitionProduct (multiplicative χ, Künneth) from PartitionProduct (additive χ, site-disjoint union).
pub mod cpt_3 {
    /// `forAll` -> `term_CPT_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CPT_3_forAll";
    /// `lhs` -> `term_CPT_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CPT_3_lhs";
    /// `rhs` -> `term_CPT_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CPT_3_rhs";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Cartesian partition product Künneth formula: Betti numbers compose via the Künneth convolution — β_k(A ⊠ B) = Σ_{i+j=k} β_i(A) · β_j(B). Routed through primitive_cartesian_nerve_betti when a CartesianProductShape marker is declared on the combined shape.
pub mod cpt_4 {
    /// `forAll` -> `term_CPT_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CPT_4_forAll";
    /// `lhs` -> `term_CPT_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CPT_4_lhs";
    /// `rhs` -> `term_CPT_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CPT_4_rhs";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Cartesian partition product entropy additivity: S(A ⊠ B) = S(A) + S(B). Matches PT_4's additive Shannon convention for independent subsystems and is consistent pointwise with IT_7a/b on the combined system (no cross-factor bilinearity required).
pub mod cpt_5 {
    /// `forAll` -> `term_CPT_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CPT_5_forAll";
    /// `lhs` -> `term_CPT_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CPT_5_lhs";
    /// `rhs` -> `term_CPT_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CPT_5_rhs";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Cartesian partition product distributes over PartitionCoproduct: A ⊠ (B + C) ≡ (A ⊠ B) + (A ⊠ C) with equality at the siteBudget, SITE_COUNT, Euler, and entropy levels simultaneously. Does NOT extend to PartitionProduct — distributing ⊠ over × fails at the site-budget level because it duplicates the outer factor.
pub mod cpt_6 {
    /// `forAll` -> `term_CPT_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CPT_6_forAll";
    /// `lhs` -> `term_CPT_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CPT_6_lhs";
    /// `rhs` -> `term_CPT_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CPT_6_rhs";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Betti-1 minimum constraint count: the minimum number of constraints needed to achieve first Betti number beta_1 = k in the constraint nerve is 2k + 1.
pub mod ts_8 {
    /// `forAll` -> `term_TS_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_8_forAll";
    /// `lhs` -> `term_TS_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_8_lhs";
    /// `rhs` -> `term_TS_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// TypeSynthesisResolver termination: the resolver terminates in at most 2^n steps for any target signature at quantum level Q_n, returning either a ConstrainedType or a ForbiddenSignature certificate.
pub mod ts_9 {
    /// `forAll` -> `term_TS_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_9_forAll";
    /// `lhs` -> `term_TS_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_9_lhs";
    /// `rhs` -> `term_TS_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// ForbiddenSignature membership criterion: a topological signature is a ForbiddenSignature iff no ConstrainedType with at most n constraints realises it at quantum level Q_n.
pub mod ts_10 {
    /// `forAll` -> `term_TS_10_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TS_10_forAll";
    /// `lhs` -> `term_TS_10_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TS_10_lhs";
    /// `rhs` -> `term_TS_10_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TS_10_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// ObstructionChain length bound: the length of the ObstructionChain from Q_j to Q_k is at most (k-j) times C(basisSize(Q_j), 3).
pub mod wt_8 {
    /// `forAll` -> `term_WT_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_8_forAll";
    /// `lhs` -> `term_WT_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_8_lhs";
    /// `rhs` -> `term_WT_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// TowerCompletenessResolver termination: the resolver terminates for any finite LiftChain within the QT_8 bound, producing a CompleteType certificate or a bounded ObstructionChain.
pub mod wt_9 {
    /// `forAll` -> `term_WT_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WT_9_forAll";
    /// `lhs` -> `term_WT_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WT_9_lhs";
    /// `rhs` -> `term_WT_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WT_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Standard coefficient ring: the coefficient ring for all psi-pipeline cohomology computations in uor.foundation is Z/2Z, consistent with MN_7.
pub mod coeff_1 {
    /// `forAll` -> `term_COEFF_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_COEFF_1_forAll";
    /// `lhs` -> `term_COEFF_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_COEFF_1_lhs";
    /// `rhs` -> `term_COEFF_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_COEFF_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// GluingObstruction feedback: given a GluingObstruction class in H^1(N(C)), the killing RefinementSuggestion adds a constraint whose pinned sites contain the intersection of the cycle-generating pair.
pub mod go_1 {
    /// `forAll` -> `term_GO_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GO_1_forAll";
    /// `lhs` -> `term_GO_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GO_1_lhs";
    /// `rhs` -> `term_GO_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GO_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Grounding re-entry free rank: for a session at full grounding, a new query q has freeRank equal to the number of q's site coordinates not already bound.
pub mod gr_6 {
    /// `forAll` -> `term_GR_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_6_forAll";
    /// `lhs` -> `term_GR_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_6_lhs";
    /// `rhs` -> `term_GR_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Grounding degree degradation: after re-entry with query q, the grounding degree becomes min(current sigma, 1 - freeRank(q)/n).
pub mod gr_7 {
    /// `forAll` -> `term_GR_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_7_forAll";
    /// `lhs` -> `term_GR_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_7_lhs";
    /// `rhs` -> `term_GR_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Amplitude index set characterization: the amplitude index set of a SuperposedSiteState over ConstrainedType T at Q_n is the set of monotone pinning trajectories consistent with T's constraints.
pub mod qm_6 {
    /// `forAll` -> `term_QM_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_QM_6_forAll";
    /// `lhs` -> `term_QM_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_QM_6_lhs";
    /// `rhs` -> `term_QM_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_QM_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `SuperpositionDomain`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/SuperpositionDomain";
}

/// Certificate issuance: every valid Transform admits a TransformCertificate attesting correct source-to-target mapping.
pub mod cic_1 {
    /// `forAll` -> `term_CIC_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CIC_1_forAll";
    /// `lhs` -> `term_CIC_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CIC_1_lhs";
    /// `rhs` -> `term_CIC_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CIC_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Certificate issuance: every metric-preserving Transform admits an IsometryCertificate attesting distance preservation.
pub mod cic_2 {
    /// `forAll` -> `term_CIC_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CIC_2_forAll";
    /// `lhs` -> `term_CIC_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CIC_2_lhs";
    /// `rhs` -> `term_CIC_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CIC_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Geometric`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Geometric";
}

/// Certificate issuance: every involutive operation f where f(f(x)) = x admits an InvolutionCertificate.
pub mod cic_3 {
    /// `forAll` -> `term_CIC_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CIC_3_forAll";
    /// `lhs` -> `term_CIC_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CIC_3_lhs";
    /// `rhs` -> `term_CIC_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CIC_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Certificate issuance: full saturation (σ = 1, freeRank = 0) admits a GroundingCertificate.
pub mod cic_4 {
    /// `forAll` -> `term_CIC_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CIC_4_forAll";
    /// `lhs` -> `term_CIC_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CIC_4_lhs";
    /// `rhs` -> `term_CIC_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CIC_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Thermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Thermodynamic";
}

/// Certificate issuance: an AR_1-ordered and DC_10-selected trace admits a GeodesicCertificate.
pub mod cic_5 {
    /// `forAll` -> `term_CIC_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CIC_5_forAll";
    /// `lhs` -> `term_CIC_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CIC_5_lhs";
    /// `rhs` -> `term_CIC_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CIC_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Certificate issuance: a MeasurementEvent verifying the von Neumann–Landauer bridge at β* = ln 2 admits a MeasurementCertificate.
pub mod cic_6 {
    /// `forAll` -> `term_CIC_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CIC_6_forAll";
    /// `lhs` -> `term_CIC_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CIC_6_lhs";
    /// `rhs` -> `term_CIC_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CIC_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `QuantumThermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/QuantumThermodynamic";
}

/// Certificate issuance: a MeasurementEvent verifying P(outcome k) = |α_k|² admits a BornRuleVerification certificate.
pub mod cic_7 {
    /// `forAll` -> `term_CIC_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CIC_7_forAll";
    /// `lhs` -> `term_CIC_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CIC_7_lhs";
    /// `rhs` -> `term_CIC_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CIC_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `QuantumThermodynamic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/QuantumThermodynamic";
}

/// Certificate issuance: shared-frame grounding that lands in the type-equivalent neighbourhood admits a GroundingCertificate.
pub mod gc_1 {
    /// `forAll` -> `term_GC_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GC_1_forAll";
    /// `lhs` -> `term_GC_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GC_1_lhs";
    /// `rhs` -> `term_GC_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GC_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Session composition validity: compose(S_A, S_B) is valid at Q_k iff all pinned-site intersections agree at every tower level Q_0 through Q_k.
pub mod gr_8 {
    /// `forAll` -> `term_GR_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_8_forAll";
    /// `lhs` -> `term_GR_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_8_lhs";
    /// `rhs` -> `term_GR_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = false;
    /// `validKMin`
    pub const VALID_KMIN: i64 = 0;
    /// `validityKind` -> `ParametricLower`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/ParametricLower";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// ContextLease disjointness: two distinct leases on the same SharedContext have non-overlapping site sets.
pub mod gr_9 {
    /// `forAll` -> `term_GR_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_9_forAll";
    /// `lhs` -> `term_GR_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_9_lhs";
    /// `rhs` -> `term_GR_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// ExecutionPolicy confluence: different execution policies on the same pending query set produce the same final resolved state (Church-Rosser for session resolution).
pub mod gr_10 {
    /// `forAll` -> `term_GR_10_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GR_10_forAll";
    /// `lhs` -> `term_GR_10_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GR_10_lhs";
    /// `rhs` -> `term_GR_10_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GR_10_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Lease partition conserves total budget: the sum of freeRank over all leases equals the SharedContext freeRank.
pub mod mc_1 {
    /// `forAll` -> `term_MC_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MC_1_forAll";
    /// `lhs` -> `term_MC_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MC_1_lhs";
    /// `rhs` -> `term_MC_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MC_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Per-lease binding monotonicity: within a leased sub-domain, freeRank decreases monotonically (SR_1 restricted to lease).
pub mod mc_2 {
    /// `forAll` -> `term_MC_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MC_2_forAll";
    /// `lhs` -> `term_MC_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MC_2_lhs";
    /// `rhs` -> `term_MC_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MC_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// General composition freeRank via inclusion-exclusion.
pub mod mc_3 {
    /// `forAll` -> `term_MC_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MC_3_forAll";
    /// `lhs` -> `term_MC_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MC_3_lhs";
    /// `rhs` -> `term_MC_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MC_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Disjoint-lease composition is additive: the intersection term vanishes when leases are site-disjoint (SR_9).
pub mod mc_4 {
    /// `forAll` -> `term_MC_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MC_4_forAll";
    /// `lhs` -> `term_MC_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MC_4_lhs";
    /// `rhs` -> `term_MC_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MC_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Policy-invariant final binding set: different execution policies produce identical SiteBinding records.
pub mod mc_5 {
    /// `forAll` -> `term_MC_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MC_5_forAll";
    /// `lhs` -> `term_MC_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MC_5_lhs";
    /// `rhs` -> `term_MC_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MC_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Full lease coverage implies composed saturation: k sessions on disjoint covering leases, each locally converged, produce a GroundedContext via composition.
pub mod mc_6 {
    /// `forAll` -> `term_MC_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MC_6_forAll";
    /// `lhs` -> `term_MC_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MC_6_lhs";
    /// `rhs` -> `term_MC_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MC_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Distributed O(1) resolution: a query against a composed GroundedContext resolves in zero steps.
pub mod mc_7 {
    /// `forAll` -> `term_MC_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MC_7_forAll";
    /// `lhs` -> `term_MC_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MC_7_lhs";
    /// `rhs` -> `term_MC_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MC_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Parallelism bound: per-session resolution work is bounded by lease size, not by total site count n.
pub mod mc_8 {
    /// `forAll` -> `term_MC_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MC_8_forAll";
    /// `lhs` -> `term_MC_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MC_8_lhs";
    /// `rhs` -> `term_MC_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MC_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Witt coordinate identification: the bit coordinates (x_0, …, x_\[n−1\]) of x ∈ Z/(2ⁿ)Z are exactly its Witt coordinates under the canonical isomorphism W_n(F_2) ≅ Z/(2ⁿ)Z.
pub mod wc_1 {
    /// `forAll` -> `term_WC_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_1_forAll";
    /// `lhs` -> `term_WC_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_1_lhs";
    /// `rhs` -> `term_WC_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Witt sum correction equals carry: the k-th Witt addition polynomial correction term S_k − x_k − y_k (mod 2) is exactly the carry c_k(x,y).
pub mod wc_2 {
    /// `forAll` -> `term_WC_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_2_forAll";
    /// `lhs` -> `term_WC_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_2_lhs";
    /// `rhs` -> `term_WC_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry recurrence is the Witt polynomial recurrence: CA_2 implements the ghost equation for S_\[k+1\] at p=2.
pub mod wc_3 {
    /// `forAll` -> `term_WC_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_3_forAll";
    /// `lhs` -> `term_WC_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_3_lhs";
    /// `rhs` -> `term_WC_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The δ-correction at level k equals the single-level carry c_\[k+1\](x,y). Each application of δ divides by 2, consuming one unit of 2-adic valuation.
pub mod wc_4 {
    /// `forAll` -> `term_WC_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_4_forAll";
    /// `lhs` -> `term_WC_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_4_lhs";
    /// `rhs` -> `term_WC_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// LiftObstruction is equivalent to δ-nonvanishing: a nontrivial LiftObstruction at Q_\[k+1\] means δ_k ≠ 0 for some element pair.
pub mod wc_5 {
    /// `forAll` -> `term_WC_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_5_forAll";
    /// `lhs` -> `term_WC_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_5_lhs";
    /// `rhs` -> `term_WC_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Metric discrepancy equals Witt defect: d_Δ(x,y) > 0 iff the ghost map correction (carry) is nonzero.
pub mod wc_6 {
    /// `forAll` -> `term_WC_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_6_forAll";
    /// `lhs` -> `term_WC_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_6_lhs";
    /// `rhs` -> `term_WC_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// D_1 is the Witt truncation order relation: succ^\[2ⁿ\](x) = x is the group relation r^\[2ⁿ\] = 1 in the Witt-Burnside ring of D_\[2∞\].
pub mod wc_7 {
    /// `forAll` -> `term_WC_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_7_forAll";
    /// `lhs` -> `term_WC_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_7_lhs";
    /// `rhs` -> `term_WC_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// D_3 is the Witt-Burnside conjugation relation: neg(succ(neg(x))) = pred(x) is srs = r⁻¹ in the pro-dihedral group.
pub mod wc_8 {
    /// `forAll` -> `term_WC_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_8_forAll";
    /// `lhs` -> `term_WC_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_8_lhs";
    /// `rhs` -> `term_WC_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// D_4 is a Witt-Burnside reflection composition: bnot(neg(x)) = pred(x) is the product of two reflections yielding inverse rotation.
pub mod wc_9 {
    /// `forAll` -> `term_WC_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_9_forAll";
    /// `lhs` -> `term_WC_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_9_lhs";
    /// `rhs` -> `term_WC_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The δ-ring Frobenius lift on W_n(F_2) is the identity map because F_2 is a perfect field of characteristic 2 (a² = a for a ∈ F_2).
pub mod wc_10 {
    /// `forAll` -> `term_WC_10_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_10_forAll";
    /// `lhs` -> `term_WC_10_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_10_lhs";
    /// `rhs` -> `term_WC_10_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_10_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The Verschiebung on W_n(F_2) is multiplication by 2: V(x) = 2x = add(x,x). This is a coordinate shift with zero Witt defect.
pub mod wc_11 {
    /// `forAll` -> `term_WC_11_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_11_forAll";
    /// `lhs` -> `term_WC_11_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_11_lhs";
    /// `rhs` -> `term_WC_11_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_11_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The δ-operator on W_n(F_2) is the squaring defect divided by 2: δ(x) = (x − mul(x,x)) / 2. Expressible entirely in existing op/ primitives (sub, mul, arithmetic right shift).
pub mod wc_12 {
    /// `forAll` -> `term_WC_12_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_WC_12_forAll";
    /// `lhs` -> `term_WC_12_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_WC_12_lhs";
    /// `rhs` -> `term_WC_12_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_WC_12_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Ostrowski product formula at p=2: |2|_2 · |2|_∞ = 1. The 2-adic and Archimedean absolute values of 2 are multiplicative inverses.
pub mod oa_1 {
    /// `forAll` -> `term_OA_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OA_1_forAll";
    /// `lhs` -> `term_OA_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OA_1_lhs";
    /// `rhs` -> `term_OA_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OA_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ArithmeticValuation`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ArithmeticValuation";
}

/// Crossing cost equals ln 2: the Archimedean image of one unit of 2-adic valuation, under the product formula, is ln 2 nats.
pub mod oa_2 {
    /// `forAll` -> `term_OA_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OA_2_forAll";
    /// `lhs` -> `term_OA_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OA_2_lhs";
    /// `rhs` -> `term_OA_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OA_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ArithmeticValuation`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ArithmeticValuation";
}

/// QM_1 grounding: the Landauer cost β* = ln 2 is the crossing cost from OA_2, derived from the prime p=2 that structures the Witt tower.
pub mod oa_3 {
    /// `forAll` -> `term_OA_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OA_3_forAll";
    /// `lhs` -> `term_OA_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OA_3_lhs";
    /// `rhs` -> `term_OA_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OA_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ArithmeticValuation`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ArithmeticValuation";
}

/// Born rule bridge (conditional on amplitude rationality): P(outcome k) = |α_k|_∞², where |·|_∞ is the Archimedean image of the 2-adic amplitude via the product formula.
pub mod oa_4 {
    /// `forAll` -> `term_OA_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OA_4_forAll";
    /// `lhs` -> `term_OA_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OA_4_lhs";
    /// `rhs` -> `term_OA_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OA_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ArithmeticValuation`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ArithmeticValuation";
}

/// Entropy per delta-level equals the crossing cost: each application of the delta-operator (division by 2) costs ln 2 nats in the Archimedean completion, which is the per-bit Landauer cost. v0.2.2 Phase C.4: grounds MultiplicationCertificate.
pub mod oa_5 {
    /// `forAll` -> `term_OA_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OA_5_forAll";
    /// `lhs` -> `term_OA_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OA_5_lhs";
    /// `rhs` -> `term_OA_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OA_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ArithmeticValuation`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ArithmeticValuation";
}

/// KanComplex(N(C)) — the constraint nerve satisfies the Kan extension condition for all horns of dimension ≤ d where d is the maximum simplex dimension of N(C).
pub mod ht_1 {
    /// `forAll` -> `term_HT_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HT_1_forAll";
    /// `lhs` -> `term_HT_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HT_1_lhs";
    /// `rhs` -> `term_HT_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HT_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Path components of nerve recover β₀: π₀(N(C)) ≅ Z^{β₀} counts the connected components of the constraint configuration.
pub mod ht_2 {
    /// `forAll` -> `term_HT_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HT_2_forAll";
    /// `lhs` -> `term_HT_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HT_2_lhs";
    /// `rhs` -> `term_HT_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HT_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// MN_6 monodromy is abelianisation of full π₁: the fundamental group π₁(N(C)) surjects onto the HolonomyGroup D_{2^n} via abelianisation.
pub mod ht_3 {
    /// `forAll` -> `term_HT_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HT_3_forAll";
    /// `lhs` -> `term_HT_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HT_3_lhs";
    /// `rhs` -> `term_HT_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HT_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Higher homotopy groups vanish above nerve dimension: π_k(N(C)) = 0 for all k > dim(N(C)), because the nerve is a finite CW-complex.
pub mod ht_4 {
    /// `forAll` -> `term_HT_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HT_4_forAll";
    /// `lhs` -> `term_HT_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HT_4_lhs";
    /// `rhs` -> `term_HT_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HT_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// 1-truncation determines flat/twisted classification: τ_{≤1}(N(C)) captures the holonomy action that distinguishes FlatType from TwistedType.
pub mod ht_5 {
    /// `forAll` -> `term_HT_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HT_5_forAll";
    /// `lhs` -> `term_HT_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HT_5_lhs";
    /// `rhs` -> `term_HT_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HT_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Trivial k-invariants beyond depth d imply spectral collapse: if κ_k is trivial for all k > d then the spectral sequence collapses at E_{d+2}.
pub mod ht_6 {
    /// `forAll` -> `term_HT_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HT_6_forAll";
    /// `lhs` -> `term_HT_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HT_6_lhs";
    /// `rhs` -> `term_HT_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HT_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Non-trivial Whitehead product implies lift obstruction: \[α, β\] ≠ 0 in π_{p+q−1} implies a non-trivial LiftObstruction that Betti numbers alone cannot detect.
pub mod ht_7 {
    /// `forAll` -> `term_HT_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HT_7_forAll";
    /// `lhs` -> `term_HT_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HT_7_lhs";
    /// `rhs` -> `term_HT_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HT_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Hurewicz isomorphism for first non-vanishing group: π_k(N(C)) ⊗ Z ≅ H_k(N(C); Z) for the smallest k with π_k ≠ 0, linking homotopy invariants to homology.
pub mod ht_8 {
    /// `forAll` -> `term_HT_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HT_8_forAll";
    /// `lhs` -> `term_HT_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HT_8_lhs";
    /// `rhs` -> `term_HT_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HT_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// ψ_7: KanComplex → PostnikovTower — compute the Postnikov truncations τ_{≤k} for k = 0, 1, …, dim(N(C)).
pub mod psi_7 {
    /// `forAll` -> `term_psi_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_psi_7_forAll";
    /// `lhs` -> `term_psi_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_psi_7_lhs";
    /// `rhs` -> `term_psi_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_psi_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// ψ_8: PostnikovTower → HomotopyGroups — extract the homotopy groups π_k from each truncation stage.
pub mod psi_8 {
    /// `forAll` -> `term_psi_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_psi_8_forAll";
    /// `lhs` -> `term_psi_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_psi_8_lhs";
    /// `rhs` -> `term_psi_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_psi_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// ψ_9: HomotopyGroups → KInvariants — compute the k-invariants κ_k classifying the Postnikov tower.
pub mod psi_9 {
    /// `forAll` -> `term_psi_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_psi_9_forAll";
    /// `lhs` -> `term_psi_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_psi_9_lhs";
    /// `rhs` -> `term_psi_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_psi_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Pipeline composition: nerve construction + Kan promotion = ψ_7 ∘ ψ_1.
pub mod hp_1 {
    /// `forAll` -> `term_HP_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HP_1_forAll";
    /// `lhs` -> `term_HP_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HP_1_lhs";
    /// `rhs` -> `term_HP_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HP_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Homotopy extraction agrees with homology on k-skeleton.
pub mod hp_2 {
    /// `forAll` -> `term_HP_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HP_2_forAll";
    /// `lhs` -> `term_HP_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HP_2_lhs";
    /// `rhs` -> `term_HP_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HP_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// k-invariant computation detects QLS_4 convergence.
pub mod hp_3 {
    /// `forAll` -> `term_HP_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HP_3_forAll";
    /// `lhs` -> `term_HP_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HP_3_lhs";
    /// `rhs` -> `term_HP_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HP_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Complexity bound for homotopy type computation.
pub mod hp_4 {
    /// `forAll` -> `term_HP_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HP_4_forAll";
    /// `lhs` -> `term_HP_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HP_4_lhs";
    /// `rhs` -> `term_HP_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HP_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Moduli space dimension equals basis size of any contained type.
pub mod md_1 {
    /// `forAll` -> `term_MD_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_1_forAll";
    /// `lhs` -> `term_MD_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_1_lhs";
    /// `rhs` -> `term_MD_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Zeroth deformation cohomology = automorphism group intersected with dihedral group.
pub mod md_2 {
    /// `forAll` -> `term_MD_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_2_forAll";
    /// `lhs` -> `term_MD_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_2_lhs";
    /// `rhs` -> `term_MD_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// First deformation cohomology = tangent space to the moduli space at T.
pub mod md_3 {
    /// `forAll` -> `term_MD_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_3_forAll";
    /// `lhs` -> `term_MD_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_3_lhs";
    /// `rhs` -> `term_MD_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Second deformation cohomology = LiftObstruction space.
pub mod md_4 {
    /// `forAll` -> `term_MD_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_4_forAll";
    /// `lhs` -> `term_MD_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_4_lhs";
    /// `rhs` -> `term_MD_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// FlatType stratum has codimension zero in the moduli space.
pub mod md_5 {
    /// `forAll` -> `term_MD_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_5_forAll";
    /// `lhs` -> `term_MD_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_5_lhs";
    /// `rhs` -> `term_MD_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// TwistedType stratum has codimension at least 1.
pub mod md_6 {
    /// `forAll` -> `term_MD_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_6_forAll";
    /// `lhs` -> `term_MD_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_6_lhs";
    /// `rhs` -> `term_MD_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// VersalDeformation existence is guaranteed when the obstruction space H² vanishes.
pub mod md_7 {
    /// `forAll` -> `term_MD_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_7_forAll";
    /// `lhs` -> `term_MD_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_7_lhs";
    /// `rhs` -> `term_MD_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// A deformation family preserves completeness iff H²(Def(T_t)) = 0 along the entire path.
pub mod md_8 {
    /// `forAll` -> `term_MD_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_8_forAll";
    /// `lhs` -> `term_MD_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_8_lhs";
    /// `rhs` -> `term_MD_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// The site of a ModuliTowerMap at T has dimension 1 when the obstruction is trivial.
pub mod md_9 {
    /// `forAll` -> `term_MD_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_9_forAll";
    /// `lhs` -> `term_MD_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_9_lhs";
    /// `rhs` -> `term_MD_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// The site of a ModuliTowerMap at T is empty iff T is a TwistedType at every level.
pub mod md_10 {
    /// `forAll` -> `term_MD_10_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MD_10_forAll";
    /// `lhs` -> `term_MD_10_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MD_10_lhs";
    /// `rhs` -> `term_MD_10_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MD_10_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// ModuliResolver boundary agrees with MorphospaceBoundary.
pub mod mr_1 {
    /// `forAll` -> `term_MR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MR_1_forAll";
    /// `lhs` -> `term_MR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MR_1_lhs";
    /// `rhs` -> `term_MR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MR_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// StratificationRecord covers every CompleteType in exactly one stratum.
pub mod mr_2 {
    /// `forAll` -> `term_MR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MR_2_forAll";
    /// `lhs` -> `term_MR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MR_2_lhs";
    /// `rhs` -> `term_MR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MR_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// ModuliResolver complexity bound.
pub mod mr_3 {
    /// `forAll` -> `term_MR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MR_3_forAll";
    /// `lhs` -> `term_MR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MR_3_lhs";
    /// `rhs` -> `term_MR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MR_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Achievable signatures correspond to membership in some HolonomyStratum.
pub mod mr_4 {
    /// `forAll` -> `term_MR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MR_4_forAll";
    /// `lhs` -> `term_MR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MR_4_lhs";
    /// `rhs` -> `term_MR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MR_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry generates at site k iff and(x_k, y_k) = 1. Extends CA_1 (addition decomposition) and WC_2 (Witt sum correction).
pub mod cy_1 {
    /// `forAll` -> `term_CY_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CY_1_forAll";
    /// `lhs` -> `term_CY_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CY_1_lhs";
    /// `rhs` -> `term_CY_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CY_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry propagates at site k iff xor(x_k, y_k) = 1 and c_k = 1. Extends CA_2 (carry recurrence) and WC_3 (Witt polynomial recurrence).
pub mod cy_2 {
    /// `forAll` -> `term_CY_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CY_2_forAll";
    /// `lhs` -> `term_CY_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CY_2_lhs";
    /// `rhs` -> `term_CY_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CY_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry kills at site k iff and(x_k, y_k) = 0 and xor(x_k, y_k) = 0. Complement of CY_1 and CY_2.
pub mod cy_3 {
    /// `forAll` -> `term_CY_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CY_3_forAll";
    /// `lhs` -> `term_CY_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CY_3_lhs";
    /// `rhs` -> `term_CY_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CY_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// d_Δ(x,y) = |carryCount(x+y) − hammingDistance(x,y)|. The metric incompatibility IS the discrepancy between carry count and Hamming distance. Strengthens WC_6.
pub mod cy_4 {
    /// `forAll` -> `term_CY_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CY_4_forAll";
    /// `lhs` -> `term_CY_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CY_4_lhs";
    /// `rhs` -> `term_CY_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CY_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Optimal encoding theorem: the encoding that minimizes Σ d_Δ over observed pairs is the one where the carry chain’s significance hierarchy matches the domain’s dependency structure.
pub mod cy_5 {
    /// `forAll` -> `term_CY_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CY_5_forAll";
    /// `lhs` -> `term_CY_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CY_5_lhs";
    /// `rhs` -> `term_CY_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CY_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site ordering theorem: d_Δ is minimized when high-significance sites (upstream in the carry chain) encode the most structurally informative observables.
pub mod cy_6 {
    /// `forAll` -> `term_CY_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CY_6_forAll";
    /// `lhs` -> `term_CY_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CY_6_lhs";
    /// `rhs` -> `term_CY_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CY_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Carry lookahead: the carry chain for n sites is computable in O(log n) using prefix computation on generate/propagate pairs.
pub mod cy_7 {
    /// `forAll` -> `term_CY_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CY_7_forAll";
    /// `lhs` -> `term_CY_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CY_7_lhs";
    /// `rhs` -> `term_CY_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CY_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// σ(C) = (n − freeRank(C)) / n. The saturation metric is the complement of free site ratio. Derives from SC_2.
pub mod bm_1 {
    /// `forAll` -> `term_BM_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BM_1_forAll";
    /// `lhs` -> `term_BM_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BM_1_lhs";
    /// `rhs` -> `term_BM_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BM_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// χ = Σ(−1)^k β_k. The Euler characteristic of the constraint nerve. Derives from IT_2.
pub mod bm_2 {
    /// `forAll` -> `term_BM_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BM_2_forAll";
    /// `lhs` -> `term_BM_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BM_2_lhs";
    /// `rhs` -> `term_BM_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BM_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Index theorem: Σκ_k − χ = S_residual / ln 2. Links all six metrics. Derives from IT_7a.
pub mod bm_3 {
    /// `forAll` -> `term_BM_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BM_3_forAll";
    /// `lhs` -> `term_BM_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BM_3_lhs";
    /// `rhs` -> `term_BM_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BM_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// J_k = 0 for pinned sites. The Jacobian vanishes on resolved sites.
pub mod bm_4 {
    /// `forAll` -> `term_BM_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BM_4_forAll";
    /// `lhs` -> `term_BM_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BM_4_lhs";
    /// `rhs` -> `term_BM_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BM_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// d_Δ > 0 iff carry ≠ 0. The metric discrepancy equals the Witt defect. Derives from WC_6.
pub mod bm_5 {
    /// `forAll` -> `term_BM_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BM_5_forAll";
    /// `lhs` -> `term_BM_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BM_5_lhs";
    /// `rhs` -> `term_BM_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BM_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// Metric composition tower: d_Δ → {σ, J_k} → β_k → χ → r. Each metric derives from previous ones.
pub mod bm_6 {
    /// `forAll` -> `term_BM_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BM_6_forAll";
    /// `lhs` -> `term_BM_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BM_6_lhs";
    /// `rhs` -> `term_BM_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BM_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `IndexTheoretic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/IndexTheoretic";
}

/// σ = lower adjoint evaluated at current type. The saturation metric is the lower adjoint of the Galois connection. Derives from SC_2.
pub mod gl_1 {
    /// `forAll` -> `term_GL_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GL_1_forAll";
    /// `lhs` -> `term_GL_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GL_1_lhs";
    /// `rhs` -> `term_GL_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GL_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// r = complement of upper adjoint image. The residual freedom is what the type closure does not reach.
pub mod gl_2 {
    /// `forAll` -> `term_GL_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GL_2_forAll";
    /// `lhs` -> `term_GL_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GL_2_lhs";
    /// `rhs` -> `term_GL_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GL_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// CompleteType = fixpoint of Galois connection, σ=1, r=0. Derives from IT_7d.
pub mod gl_3 {
    /// `forAll` -> `term_GL_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GL_3_forAll";
    /// `lhs` -> `term_GL_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GL_3_lhs";
    /// `rhs` -> `term_GL_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GL_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Type refinement = ascending in type lattice = descending in site freedom. The Galois connection reverses order.
pub mod gl_4 {
    /// `forAll` -> `term_GL_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_GL_4_forAll";
    /// `lhs` -> `term_GL_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_GL_4_lhs";
    /// `rhs` -> `term_GL_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_GL_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// nerve(C₁ ∪ C₂) = nerve(C₁) ∪ nerve(C₂) for disjoint constraint domains.
pub mod nv_1 {
    /// `forAll` -> `term_NV_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_NV_1_forAll";
    /// `lhs` -> `term_NV_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_NV_1_lhs";
    /// `rhs` -> `term_NV_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_NV_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Mayer–Vietoris: β_k(C₁ ∪ C₂) computable from parts and intersection.
pub mod nv_2 {
    /// `forAll` -> `term_NV_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_NV_2_forAll";
    /// `lhs` -> `term_NV_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_NV_2_lhs";
    /// `rhs` -> `term_NV_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_NV_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Single constraint addition: Δβ_k ∈ {−1, 0, +1} per dimension.
pub mod nv_3 {
    /// `forAll` -> `term_NV_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_NV_3_forAll";
    /// `lhs` -> `term_NV_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_NV_3_lhs";
    /// `rhs` -> `term_NV_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_NV_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Constraint accumulation monotonicity: β_k non-increasing under SR_1. Derives from SR_1.
pub mod nv_4 {
    /// `forAll` -> `term_NV_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_NV_4_forAll";
    /// `lhs` -> `term_NV_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_NV_4_lhs";
    /// `rhs` -> `term_NV_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_NV_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// ScalarType grounding: quantize(value, range, bits) produces ring element where d_R reflects value proximity.
pub mod sd_1 {
    /// `forAll` -> `term_SD_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SD_1_forAll";
    /// `lhs` -> `term_SD_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SD_1_lhs";
    /// `rhs` -> `term_SD_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SD_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// SymbolType grounding: argmin_{encoding} Σ d_Δ over observed pairs (CY_5).
pub mod sd_2 {
    /// `forAll` -> `term_SD_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SD_2_forAll";
    /// `lhs` -> `term_SD_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SD_2_lhs";
    /// `rhs` -> `term_SD_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SD_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// SequenceType = free monoid on element type with backbone constraint.
pub mod sd_3 {
    /// `forAll` -> `term_SD_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SD_3_forAll";
    /// `lhs` -> `term_SD_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SD_3_lhs";
    /// `rhs` -> `term_SD_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SD_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// TupleType site count = Σ field site counts, site ordering follows CY_6.
pub mod sd_4 {
    /// `forAll` -> `term_SD_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SD_4_forAll";
    /// `lhs` -> `term_SD_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SD_4_lhs";
    /// `rhs` -> `term_SD_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SD_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// GraphType constraint nerve = graph nerve, β_k equality.
pub mod sd_5 {
    /// `forAll` -> `term_SD_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SD_5_forAll";
    /// `lhs` -> `term_SD_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SD_5_lhs";
    /// `rhs` -> `term_SD_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SD_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// SetType d_Δ invariant under element permutation, D_{2n} symmetry.
pub mod sd_6 {
    /// `forAll` -> `term_SD_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SD_6_forAll";
    /// `lhs` -> `term_SD_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SD_6_lhs";
    /// `rhs` -> `term_SD_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SD_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// TreeType β_1=0, β_0=1 topological constraints.
pub mod sd_7 {
    /// `forAll` -> `term_SD_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SD_7_forAll";
    /// `lhs` -> `term_SD_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SD_7_lhs";
    /// `rhs` -> `term_SD_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SD_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// TableType = SequenceType(TupleType(S)), functorial decomposition.
pub mod sd_8 {
    /// `forAll` -> `term_SD_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SD_8_forAll";
    /// `lhs` -> `term_SD_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SD_8_lhs";
    /// `rhs` -> `term_SD_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SD_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Dispatch determinism: same query and same registry always yield the same resolver.
pub mod dd_1 {
    /// `forAll` -> `term_DD_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DD_1_forAll";
    /// `lhs` -> `term_DD_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DD_1_lhs";
    /// `rhs` -> `term_DD_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DD_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Dispatch coverage: every query in the registry domain has a matching resolver.
pub mod dd_2 {
    /// `forAll` -> `term_DD_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DD_2_forAll";
    /// `lhs` -> `term_DD_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DD_2_lhs";
    /// `rhs` -> `term_DD_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DD_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Inference idempotence: ι(ι(s,C),C) = ι(s,C) on GroundedContext.
pub mod pi_1 {
    /// `forAll` -> `term_PI_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PI_1_forAll";
    /// `lhs` -> `term_PI_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PI_1_lhs";
    /// `rhs` -> `term_PI_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PI_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Inference soundness: ι(s,C) resolves to a type consistent with C.
pub mod pi_2 {
    /// `forAll` -> `term_PI_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PI_2_forAll";
    /// `lhs` -> `term_PI_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PI_2_lhs";
    /// `rhs` -> `term_PI_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PI_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Inference composition: ι = P ∘ Π ∘ G (references phi_4).
pub mod pi_3 {
    /// `forAll` -> `term_PI_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PI_3_forAll";
    /// `lhs` -> `term_PI_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PI_3_lhs";
    /// `rhs` -> `term_PI_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PI_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Inference complexity: O(n) worst case, O(1) on CompleteType.
pub mod pi_4 {
    /// `forAll` -> `term_PI_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PI_4_forAll";
    /// `lhs` -> `term_PI_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PI_4_lhs";
    /// `rhs` -> `term_PI_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PI_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Inference coherence: roundTrip(P(Π(G(s)))) = s.
pub mod pi_5 {
    /// `forAll` -> `term_PI_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PI_5_forAll";
    /// `lhs` -> `term_PI_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PI_5_lhs";
    /// `rhs` -> `term_PI_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PI_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Accumulation permutation invariance: accumulating bindings in any order yields the same saturated context (derives from SR_10).
pub mod pa_1 {
    /// `forAll` -> `term_PA_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PA_1_forAll";
    /// `lhs` -> `term_PA_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PA_1_lhs";
    /// `rhs` -> `term_PA_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PA_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Accumulation monotonicity: α(b,C) ⊇ C (the context only grows, never loses bindings). Derives from SR_1.
pub mod pa_2 {
    /// `forAll` -> `term_PA_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PA_2_forAll";
    /// `lhs` -> `term_PA_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PA_2_lhs";
    /// `rhs` -> `term_PA_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PA_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Accumulation soundness: α(b,C) preserves all previously satisfied constraints. Derives from SR_2.
pub mod pa_3 {
    /// `forAll` -> `term_PA_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PA_3_forAll";
    /// `lhs` -> `term_PA_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PA_3_lhs";
    /// `rhs` -> `term_PA_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PA_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Accumulation base preservation: α does not modify previously pinned sites.
pub mod pa_4 {
    /// `forAll` -> `term_PA_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PA_4_forAll";
    /// `lhs` -> `term_PA_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PA_4_lhs";
    /// `rhs` -> `term_PA_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PA_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Accumulation identity: α(∅, C) = C.
pub mod pa_5 {
    /// `forAll` -> `term_PA_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PA_5_forAll";
    /// `lhs` -> `term_PA_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PA_5_lhs";
    /// `rhs` -> `term_PA_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PA_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Lease disjointness: partitioned leases have pairwise disjoint site sets (derives from SR_9).
pub mod pl_1 {
    /// `forAll` -> `term_PL_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PL_1_forAll";
    /// `lhs` -> `term_PL_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PL_1_lhs";
    /// `rhs` -> `term_PL_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PL_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Lease conservation: union of all leases equals the original shared context (derives from MC_1).
pub mod pl_2 {
    /// `forAll` -> `term_PL_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PL_2_forAll";
    /// `lhs` -> `term_PL_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PL_2_lhs";
    /// `rhs` -> `term_PL_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PL_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Lease coverage: every site in the shared context appears in exactly one lease (derives from MC_6).
pub mod pl_3 {
    /// `forAll` -> `term_PL_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PL_3_forAll";
    /// `lhs` -> `term_PL_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PL_3_lhs";
    /// `rhs` -> `term_PL_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PL_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Composition validity: κ(S₁,S₂) is a valid session if S₁,S₂ have disjoint leases (derives from SR_8).
pub mod pk_1 {
    /// `forAll` -> `term_PK_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PK_1_forAll";
    /// `lhs` -> `term_PK_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PK_1_lhs";
    /// `rhs` -> `term_PK_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PK_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Distributed resolution: resolving in κ(S₁,S₂) equals resolving in S₁ or S₂ independently (derives from MC_7).
pub mod pk_2 {
    /// `forAll` -> `term_PK_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PK_2_forAll";
    /// `lhs` -> `term_PK_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PK_2_lhs";
    /// `rhs` -> `term_PK_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PK_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Pipeline unification: κ(λₖ(α*(ι(s,·))),C) = resolve(s,C). The full composed pipeline equals the top-level resolution function.
pub mod pp_1 {
    /// `forAll` -> `term_PP_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PP_1_forAll";
    /// `lhs` -> `term_PP_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PP_1_lhs";
    /// `rhs` -> `term_PP_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PP_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Stage 0 initializes state vector to 1.
pub mod pe_1 {
    /// `forAll` -> `term_PE_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PE_1_forAll";
    /// `lhs` -> `term_PE_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PE_1_lhs";
    /// `rhs` -> `term_PE_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PE_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stage 1 dispatches resolver (δ selects).
pub mod pe_2 {
    /// `forAll` -> `term_PE_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PE_2_forAll";
    /// `lhs` -> `term_PE_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PE_2_lhs";
    /// `rhs` -> `term_PE_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PE_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stage 2 produces valid ring address (G grounds).
pub mod pe_3 {
    /// `forAll` -> `term_PE_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PE_3_forAll";
    /// `lhs` -> `term_PE_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PE_3_lhs";
    /// `rhs` -> `term_PE_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PE_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stage 3 resolves constraints (Π terminates).
pub mod pe_4 {
    /// `forAll` -> `term_PE_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PE_4_forAll";
    /// `lhs` -> `term_PE_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PE_4_lhs";
    /// `rhs` -> `term_PE_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PE_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stage 4 accumulates without contradiction (α consistent).
pub mod pe_5 {
    /// `forAll` -> `term_PE_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PE_5_forAll";
    /// `lhs` -> `term_PE_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PE_5_lhs";
    /// `rhs` -> `term_PE_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PE_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stage 5 extracts coherent output (P projects).
pub mod pe_6 {
    /// `forAll` -> `term_PE_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PE_6_forAll";
    /// `lhs` -> `term_PE_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PE_6_lhs";
    /// `rhs` -> `term_PE_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PE_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Full pipeline is the composition PE_6 ∘ … ∘ PE_1.
pub mod pe_7 {
    /// `forAll` -> `term_PE_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PE_7_forAll";
    /// `lhs` -> `term_PE_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PE_7_lhs";
    /// `rhs` -> `term_PE_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PE_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Phase rotation Ω^k at stage k.
pub mod pm_1 {
    /// `forAll` -> `term_PM_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PM_1_forAll";
    /// `lhs` -> `term_PM_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PM_1_lhs";
    /// `rhs` -> `term_PM_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PM_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Phase gate checks Ω^k at boundary.
pub mod pm_2 {
    /// `forAll` -> `term_PM_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PM_2_forAll";
    /// `lhs` -> `term_PM_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PM_2_lhs";
    /// `rhs` -> `term_PM_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PM_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Gate failure triggers complex conjugate rollback.
pub mod pm_3 {
    /// `forAll` -> `term_PM_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PM_3_forAll";
    /// `lhs` -> `term_PM_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PM_3_lhs";
    /// `rhs` -> `term_PM_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PM_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Rollback is involutory: (z̄)̄ = z.
pub mod pm_4 {
    /// `forAll` -> `term_PM_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PM_4_forAll";
    /// `lhs` -> `term_PM_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PM_4_lhs";
    /// `rhs` -> `term_PM_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PM_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Epoch boundary preserves saturation.
pub mod pm_5 {
    /// `forAll` -> `term_PM_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PM_5_forAll";
    /// `lhs` -> `term_PM_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PM_5_lhs";
    /// `rhs` -> `term_PM_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PM_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Service window provides base context.
pub mod pm_6 {
    /// `forAll` -> `term_PM_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PM_6_forAll";
    /// `lhs` -> `term_PM_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PM_6_lhs";
    /// `rhs` -> `term_PM_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PM_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Machine is deterministic given initial state.
pub mod pm_7 {
    /// `forAll` -> `term_PM_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PM_7_forAll";
    /// `lhs` -> `term_PM_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PM_7_lhs";
    /// `rhs` -> `term_PM_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PM_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stage transition requires guard satisfaction.
pub mod er_1 {
    /// `forAll` -> `term_ER_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ER_1_forAll";
    /// `lhs` -> `term_ER_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ER_1_lhs";
    /// `rhs` -> `term_ER_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ER_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Effect application is atomic.
pub mod er_2 {
    /// `forAll` -> `term_ER_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ER_2_forAll";
    /// `lhs` -> `term_ER_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ER_2_lhs";
    /// `rhs` -> `term_ER_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ER_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Guard evaluation is side-effect-free.
pub mod er_3 {
    /// `forAll` -> `term_ER_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ER_3_forAll";
    /// `lhs` -> `term_ER_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ER_3_lhs";
    /// `rhs` -> `term_ER_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ER_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Effect composition is order-independent within a stage.
pub mod er_4 {
    /// `forAll` -> `term_ER_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_ER_4_forAll";
    /// `lhs` -> `term_ER_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_ER_4_lhs";
    /// `rhs` -> `term_ER_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_ER_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Epoch boundary resets free sites.
pub mod ea_1 {
    /// `forAll` -> `term_EA_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EA_1_forAll";
    /// `lhs` -> `term_EA_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EA_1_lhs";
    /// `rhs` -> `term_EA_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EA_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Grounding carries across epochs.
pub mod ea_2 {
    /// `forAll` -> `term_EA_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EA_2_forAll";
    /// `lhs` -> `term_EA_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EA_2_lhs";
    /// `rhs` -> `term_EA_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EA_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Service window bounds context size.
pub mod ea_3 {
    /// `forAll` -> `term_EA_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EA_3_forAll";
    /// `lhs` -> `term_EA_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EA_3_lhs";
    /// `rhs` -> `term_EA_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EA_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Epoch admits one datum or one refinement pass.
pub mod ea_4 {
    /// `forAll` -> `term_EA_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EA_4_forAll";
    /// `lhs` -> `term_EA_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EA_4_lhs";
    /// `rhs` -> `term_EA_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EA_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Adjacent stages with compatible guards may fuse.
pub mod oe_1 {
    /// `forAll` -> `term_OE_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OE_1_forAll";
    /// `lhs` -> `term_OE_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OE_1_lhs";
    /// `rhs` -> `term_OE_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OE_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Independent effects commute.
pub mod oe_2 {
    /// `forAll` -> `term_OE_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OE_2_forAll";
    /// `lhs` -> `term_OE_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OE_2_lhs";
    /// `rhs` -> `term_OE_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OE_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Disjoint leases parallelize.
pub mod oe_3 {
    /// `forAll` -> `term_OE_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OE_3_forAll";
    /// `lhs` -> `term_OE_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OE_3_lhs";
    /// `rhs` -> `term_OE_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OE_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stage fusion preserves semantics.
pub mod oe_4a {
    /// `forAll` -> `term_OE_4a_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OE_4a_forAll";
    /// `lhs` -> `term_OE_4a_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OE_4a_lhs";
    /// `rhs` -> `term_OE_4a_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OE_4a_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Effect commutation preserves outcome.
pub mod oe_4b {
    /// `forAll` -> `term_OE_4b_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OE_4b_forAll";
    /// `lhs` -> `term_OE_4b_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OE_4b_lhs";
    /// `rhs` -> `term_OE_4b_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OE_4b_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Lease parallelism preserves coverage.
pub mod oe_4c {
    /// `forAll` -> `term_OE_4c_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OE_4c_forAll";
    /// `lhs` -> `term_OE_4c_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OE_4c_lhs";
    /// `rhs` -> `term_OE_4c_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OE_4c_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Each stage has bounded cost.
pub mod cs_1 {
    /// `forAll` -> `term_CS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CS_1_forAll";
    /// `lhs` -> `term_CS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CS_1_lhs";
    /// `rhs` -> `term_CS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CS_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Pipeline cost = sum of stage costs.
pub mod cs_2 {
    /// `forAll` -> `term_CS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CS_2_forAll";
    /// `lhs` -> `term_CS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CS_2_lhs";
    /// `rhs` -> `term_CS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CS_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Rollback cost is at most forward cost.
pub mod cs_3 {
    /// `forAll` -> `term_CS_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CS_3_forAll";
    /// `lhs` -> `term_CS_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CS_3_lhs";
    /// `rhs` -> `term_CS_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CS_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Preflight cost is O(1).
pub mod cs_4 {
    /// `forAll` -> `term_CS_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CS_4_forAll";
    /// `lhs` -> `term_CS_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CS_4_lhs";
    /// `rhs` -> `term_CS_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CS_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Total reduction cost bounded by n × stage_max_cost.
pub mod cs_5 {
    /// `forAll` -> `term_CS_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CS_5_forAll";
    /// `lhs` -> `term_CS_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CS_5_lhs";
    /// `rhs` -> `term_CS_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CS_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Budget solvency rejection: a CompileUnit whose declared thermodynamicBudget is strictly less than the Landauer minimum (bitsWidth(Q_k) × ln 2) is rejected at the BudgetSolvencyCheck preflight.
pub mod cs_6 {
    /// `forAll` -> `term_CS_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CS_6_forAll";
    /// `lhs` -> `term_CS_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CS_6_lhs";
    /// `rhs` -> `term_CS_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CS_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Unit address identity: the unitAddress of a CompileUnit is the u:Element computed by hashing the canonical byte serialization of the root term’s transitive closure.
pub mod cs_7 {
    /// `forAll` -> `term_CS_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CS_7_forAll";
    /// `lhs` -> `term_CS_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CS_7_lhs";
    /// `rhs` -> `term_CS_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CS_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Every pending query eventually reaches a stage gate.
pub mod fa_1 {
    /// `forAll` -> `term_FA_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FA_1_forAll";
    /// `lhs` -> `term_FA_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FA_1_lhs";
    /// `rhs` -> `term_FA_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FA_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// No starvation under bounded epoch admission.
pub mod fa_2 {
    /// `forAll` -> `term_FA_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FA_2_forAll";
    /// `lhs` -> `term_FA_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FA_2_lhs";
    /// `rhs` -> `term_FA_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FA_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Fair lease allocation under disjoint composition.
pub mod fa_3 {
    /// `forAll` -> `term_FA_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FA_3_forAll";
    /// `lhs` -> `term_FA_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FA_3_lhs";
    /// `rhs` -> `term_FA_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FA_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Service window bounds context memory.
pub mod sw_1 {
    /// `forAll` -> `term_SW_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SW_1_forAll";
    /// `lhs` -> `term_SW_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SW_1_lhs";
    /// `rhs` -> `term_SW_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SW_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Window slide preserves saturation invariant.
pub mod sw_2 {
    /// `forAll` -> `term_SW_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SW_2_forAll";
    /// `lhs` -> `term_SW_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SW_2_lhs";
    /// `rhs` -> `term_SW_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SW_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Evicted epochs release lease resources.
pub mod sw_3 {
    /// `forAll` -> `term_SW_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SW_3_forAll";
    /// `lhs` -> `term_SW_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SW_3_lhs";
    /// `rhs` -> `term_SW_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SW_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Window size ≥ 1 (non-empty).
pub mod sw_4 {
    /// `forAll` -> `term_SW_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SW_4_forAll";
    /// `lhs` -> `term_SW_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SW_4_lhs";
    /// `rhs` -> `term_SW_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SW_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Suspended lease preserves pinned state.
pub mod ls_1 {
    /// `forAll` -> `term_LS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LS_1_forAll";
    /// `lhs` -> `term_LS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LS_1_lhs";
    /// `rhs` -> `term_LS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LS_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Lease expiry triggers resource release.
pub mod ls_2 {
    /// `forAll` -> `term_LS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LS_2_forAll";
    /// `lhs` -> `term_LS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LS_2_lhs";
    /// `rhs` -> `term_LS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LS_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Checkpoint restore is idempotent.
pub mod ls_3 {
    /// `forAll` -> `term_LS_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LS_3_forAll";
    /// `lhs` -> `term_LS_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LS_3_lhs";
    /// `rhs` -> `term_LS_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LS_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Active → Suspended → Active round-trip preserves state.
pub mod ls_4 {
    /// `forAll` -> `term_LS_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LS_4_forAll";
    /// `lhs` -> `term_LS_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LS_4_lhs";
    /// `rhs` -> `term_LS_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LS_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// AllOrNothing transaction rolls back on any failure.
pub mod tj_1 {
    /// `forAll` -> `term_TJ_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TJ_1_forAll";
    /// `lhs` -> `term_TJ_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TJ_1_lhs";
    /// `rhs` -> `term_TJ_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TJ_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// BestEffort transaction commits partial results.
pub mod tj_2 {
    /// `forAll` -> `term_TJ_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TJ_2_forAll";
    /// `lhs` -> `term_TJ_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TJ_2_lhs";
    /// `rhs` -> `term_TJ_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TJ_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Transaction atomicity within a single epoch.
pub mod tj_3 {
    /// `forAll` -> `term_TJ_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_TJ_3_forAll";
    /// `lhs` -> `term_TJ_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_TJ_3_lhs";
    /// `rhs` -> `term_TJ_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_TJ_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Partial saturation is monotonically non-decreasing across stages.
pub mod ap_1 {
    /// `forAll` -> `term_AP_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AP_1_forAll";
    /// `lhs` -> `term_AP_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AP_1_lhs";
    /// `rhs` -> `term_AP_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AP_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Approximation quality improves with additional epochs.
pub mod ap_2 {
    /// `forAll` -> `term_AP_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AP_2_forAll";
    /// `lhs` -> `term_AP_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AP_2_lhs";
    /// `rhs` -> `term_AP_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AP_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Deferred queries are eventually processed or explicitly dropped.
pub mod ap_3 {
    /// `forAll` -> `term_AP_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AP_3_forAll";
    /// `lhs` -> `term_AP_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AP_3_lhs";
    /// `rhs` -> `term_AP_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AP_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Ω⁶ = −1: reduction converges in 6 stages (phase half-turn).
pub mod ec_1 {
    /// `forAll` -> `term_EC_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EC_1_forAll";
    /// `lhs` -> `term_EC_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EC_1_lhs";
    /// `rhs` -> `term_EC_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EC_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Complex conjugate rollback involutory: (z̄)̄ = z.
pub mod ec_2 {
    /// `forAll` -> `term_EC_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EC_2_forAll";
    /// `lhs` -> `term_EC_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EC_2_lhs";
    /// `rhs` -> `term_EC_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EC_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Pairwise convergence: commutator converges to identity.
pub mod ec_3 {
    /// `forAll` -> `term_EC_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EC_3_forAll";
    /// `lhs` -> `term_EC_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EC_3_lhs";
    /// `rhs` -> `term_EC_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EC_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Triple convergence: associator converges to zero.
pub mod ec_4 {
    /// `forAll` -> `term_EC_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EC_4_forAll";
    /// `lhs` -> `term_EC_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EC_4_lhs";
    /// `rhs` -> `term_EC_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EC_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Associator monotonicity: associator norm non-increasing.
pub mod ec_4a {
    /// `forAll` -> `term_EC_4a_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EC_4a_forAll";
    /// `lhs` -> `term_EC_4a_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EC_4a_lhs";
    /// `rhs` -> `term_EC_4a_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EC_4a_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Associator finiteness: reaches 0 in bounded steps.
pub mod ec_4b {
    /// `forAll` -> `term_EC_4b_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EC_4b_forAll";
    /// `lhs` -> `term_EC_4b_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EC_4b_lhs";
    /// `rhs` -> `term_EC_4b_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EC_4b_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Associator vanishing implies associativity on resolved site space.
pub mod ec_4c {
    /// `forAll` -> `term_EC_4c_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EC_4c_forAll";
    /// `lhs` -> `term_EC_4c_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EC_4c_lhs";
    /// `rhs` -> `term_EC_4c_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EC_4c_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Adams termination: no convergence level beyond L3_Self.
pub mod ec_5 {
    /// `forAll` -> `term_EC_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_EC_5_forAll";
    /// `lhs` -> `term_EC_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_EC_5_lhs";
    /// `rhs` -> `term_EC_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_EC_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Cayley-Dickson R→C: adjoin i with i²=−1, conjugation (a+bi)* = a−bi.
pub mod da_1 {
    /// `forAll` -> `term_DA_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DA_1_forAll";
    /// `lhs` -> `term_DA_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DA_1_lhs";
    /// `rhs` -> `term_DA_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DA_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Cayley-Dickson C→H: adjoin j with j²=−1, ij=k, ji=−k, k²=−1.
pub mod da_2 {
    /// `forAll` -> `term_DA_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DA_2_forAll";
    /// `lhs` -> `term_DA_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DA_2_lhs";
    /// `rhs` -> `term_DA_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DA_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Cayley-Dickson H→O: adjoin l, Fano plane products, associativity fails.
pub mod da_3 {
    /// `forAll` -> `term_DA_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DA_3_forAll";
    /// `lhs` -> `term_DA_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DA_3_lhs";
    /// `rhs` -> `term_DA_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DA_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Adams theorem: no normed division algebra of dimension 16 exists.
pub mod da_4 {
    /// `forAll` -> `term_DA_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DA_4_forAll";
    /// `lhs` -> `term_DA_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DA_4_lhs";
    /// `rhs` -> `term_DA_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DA_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Convergence level k lives in k-th division algebra: L0 in R, L1 in C, L2 in H, L3 in O.
pub mod da_5 {
    /// `forAll` -> `term_DA_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DA_5_forAll";
    /// `lhs` -> `term_DA_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DA_5_lhs";
    /// `rhs` -> `term_DA_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DA_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Commutator vanishes iff algebra at that level is commutative.
pub mod da_6 {
    /// `forAll` -> `term_DA_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DA_6_forAll";
    /// `lhs` -> `term_DA_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DA_6_lhs";
    /// `rhs` -> `term_DA_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DA_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Associator vanishes iff algebra at that level is associative.
pub mod da_7 {
    /// `forAll` -> `term_DA_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DA_7_forAll";
    /// `lhs` -> `term_DA_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DA_7_lhs";
    /// `rhs` -> `term_DA_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DA_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// d_Δ as interaction cost between entities.
pub mod in_1 {
    /// `forAll` -> `term_IN_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_1_forAll";
    /// `lhs` -> `term_IN_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_1_lhs";
    /// `rhs` -> `term_IN_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Disjoint leases imply commutator = 0.
pub mod in_2 {
    /// `forAll` -> `term_IN_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_2_forAll";
    /// `lhs` -> `term_IN_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_2_lhs";
    /// `rhs` -> `term_IN_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Shared sites imply commutator > 0.
pub mod in_3 {
    /// `forAll` -> `term_IN_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_3_forAll";
    /// `lhs` -> `term_IN_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_3_lhs";
    /// `rhs` -> `term_IN_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// SR_8 implies negotiation converges (commutator decreases monotonically).
pub mod in_4 {
    /// `forAll` -> `term_IN_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_4_forAll";
    /// `lhs` -> `term_IN_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_4_lhs";
    /// `rhs` -> `term_IN_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Convergent negotiation selects U(1) ⊂ SU(2).
pub mod in_5 {
    /// `forAll` -> `term_IN_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_5_forAll";
    /// `lhs` -> `term_IN_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_5_lhs";
    /// `rhs` -> `term_IN_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Outcome space of pairwise negotiation is S².
pub mod in_6 {
    /// `forAll` -> `term_IN_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_6_forAll";
    /// `lhs` -> `term_IN_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_6_lhs";
    /// `rhs` -> `term_IN_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Mutual modeling selects H ⊂ O.
pub mod in_7 {
    /// `forAll` -> `term_IN_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_7_forAll";
    /// `lhs` -> `term_IN_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_7_lhs";
    /// `rhs` -> `term_IN_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Interaction nerve β_k bounds coupling complexity at dimension k.
pub mod in_8 {
    /// `forAll` -> `term_IN_8_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_8_forAll";
    /// `lhs` -> `term_IN_8_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_8_lhs";
    /// `rhs` -> `term_IN_8_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_8_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// β_2(nerve) × max_disagreement bounds associator norm.
pub mod in_9 {
    /// `forAll` -> `term_IN_9_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IN_9_forAll";
    /// `lhs` -> `term_IN_9_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IN_9_lhs";
    /// `rhs` -> `term_IN_9_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IN_9_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// δ-ι-κ non-associativity: δ reads registry written by κ.
pub mod as_1 {
    /// `forAll` -> `term_AS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AS_1_forAll";
    /// `lhs` -> `term_AS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AS_1_lhs";
    /// `rhs` -> `term_AS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AS_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// ι-α-λ non-associativity: λ reads lease state written by α.
pub mod as_2 {
    /// `forAll` -> `term_AS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AS_2_forAll";
    /// `lhs` -> `term_AS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AS_2_lhs";
    /// `rhs` -> `term_AS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AS_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// λ-κ-δ non-associativity: δ reads state written by κ.
pub mod as_3 {
    /// `forAll` -> `term_AS_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AS_3_forAll";
    /// `lhs` -> `term_AS_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AS_3_lhs";
    /// `rhs` -> `term_AS_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AS_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Root cause: non-associativity from read-write interleaving through mediating entity.
pub mod as_4 {
    /// `forAll` -> `term_AS_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_AS_4_forAll";
    /// `lhs` -> `term_AS_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_AS_4_lhs";
    /// `rhs` -> `term_AS_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_AS_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `ComposedAlgebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/ComposedAlgebraic";
}

/// Unit law: I ⊗ A ≅ A ≅ A ⊗ I.
pub mod mo_1 {
    /// `forAll` -> `term_MO_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MO_1_forAll";
    /// `lhs` -> `term_MO_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MO_1_lhs";
    /// `rhs` -> `term_MO_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MO_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Associativity: (A⊗B)⊗C ≅ A⊗(B⊗C).
pub mod mo_2 {
    /// `forAll` -> `term_MO_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MO_2_forAll";
    /// `lhs` -> `term_MO_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MO_2_lhs";
    /// `rhs` -> `term_MO_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MO_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Certificate composition: cert(A⊗B) contains cert(A) and cert(B).
pub mod mo_3 {
    /// `forAll` -> `term_MO_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MO_3_forAll";
    /// `lhs` -> `term_MO_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MO_3_lhs";
    /// `rhs` -> `term_MO_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MO_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// σ(A⊗B) ≥ max(σ(A), σ(B)): sequential composition does not lose saturation.
pub mod mo_4 {
    /// `forAll` -> `term_MO_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MO_4_forAll";
    /// `lhs` -> `term_MO_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MO_4_lhs";
    /// `rhs` -> `term_MO_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MO_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// r(A⊗B) ≤ min(r(A), r(B)): residual can only shrink under sequential composition.
pub mod mo_5 {
    /// `forAll` -> `term_MO_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_MO_5_forAll";
    /// `lhs` -> `term_MO_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_MO_5_lhs";
    /// `rhs` -> `term_MO_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_MO_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Site additivity: siteCount(F(G)) = F.sites + Σ_i G_i.sites.
pub mod op_1 {
    /// `forAll` -> `term_OP_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OP_1_forAll";
    /// `lhs` -> `term_OP_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OP_1_lhs";
    /// `rhs` -> `term_OP_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OP_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Grounding distributivity: grounding(F(G(x))) = F.ground(G.ground(x)).
pub mod op_2 {
    /// `forAll` -> `term_OP_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OP_2_forAll";
    /// `lhs` -> `term_OP_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OP_2_lhs";
    /// `rhs` -> `term_OP_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OP_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// d_Δ decomposition: d_Δ(F(G)) decomposes into outer + inner d_Δ.
pub mod op_3 {
    /// `forAll` -> `term_OP_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OP_3_forAll";
    /// `lhs` -> `term_OP_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OP_3_lhs";
    /// `rhs` -> `term_OP_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OP_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Table(Tuple(fields)): standard tabular data structure decomposition.
pub mod op_4 {
    /// `forAll` -> `term_OP_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OP_4_forAll";
    /// `lhs` -> `term_OP_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OP_4_lhs";
    /// `rhs` -> `term_OP_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OP_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Tree(leaves): standard hierarchical data structure (AST, XML, JSON).
pub mod op_5 {
    /// `forAll` -> `term_OP_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_OP_5_forAll";
    /// `lhs` -> `term_OP_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_OP_5_lhs";
    /// `rhs` -> `term_OP_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_OP_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Pinning decrements free count by exactly 1.
pub mod fx_1 {
    /// `forAll` -> `term_FX_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FX_1_forAll";
    /// `lhs` -> `term_FX_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FX_1_lhs";
    /// `rhs` -> `term_FX_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FX_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Unbinding increments free count by exactly 1.
pub mod fx_2 {
    /// `forAll` -> `term_FX_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FX_2_forAll";
    /// `lhs` -> `term_FX_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FX_2_lhs";
    /// `rhs` -> `term_FX_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FX_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Phase effects preserve site budget.
pub mod fx_3 {
    /// `forAll` -> `term_FX_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FX_3_forAll";
    /// `lhs` -> `term_FX_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FX_3_lhs";
    /// `rhs` -> `term_FX_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FX_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Disjoint effects commute.
pub mod fx_4 {
    /// `forAll` -> `term_FX_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FX_4_forAll";
    /// `lhs` -> `term_FX_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FX_4_lhs";
    /// `rhs` -> `term_FX_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FX_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Composite free-count delta is additive.
pub mod fx_5 {
    /// `forAll` -> `term_FX_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FX_5_forAll";
    /// `lhs` -> `term_FX_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FX_5_lhs";
    /// `rhs` -> `term_FX_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FX_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Every ReversibleEffect has an inverse (PinningEffect⁻¹ = UnbindingEffect on same site, PhaseEffect⁻¹ = conjugate phase).
pub mod fx_6 {
    /// `forAll` -> `term_FX_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FX_6_forAll";
    /// `lhs` -> `term_FX_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FX_6_lhs";
    /// `rhs` -> `term_FX_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FX_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// External effects must match their declared shape.
pub mod fx_7 {
    /// `forAll` -> `term_FX_7_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FX_7_forAll";
    /// `lhs` -> `term_FX_7_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FX_7_lhs";
    /// `rhs` -> `term_FX_7_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FX_7_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Every predicate is total: evaluation terminates for all inputs.
pub mod pr_1 {
    /// `forAll` -> `term_PR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PR_1_forAll";
    /// `lhs` -> `term_PR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PR_1_lhs";
    /// `rhs` -> `term_PR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PR_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Every predicate is pure: evaluation does not modify state.
pub mod pr_2 {
    /// `forAll` -> `term_PR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PR_2_forAll";
    /// `lhs` -> `term_PR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PR_2_lhs";
    /// `rhs` -> `term_PR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PR_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Exhaustive + mutually exclusive dispatch is deterministic.
pub mod pr_3 {
    /// `forAll` -> `term_PR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PR_3_forAll";
    /// `lhs` -> `term_PR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PR_3_lhs";
    /// `rhs` -> `term_PR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PR_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Match evaluation is deterministic given exhaustive, ordered arms.
pub mod pr_4 {
    /// `forAll` -> `term_PR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PR_4_forAll";
    /// `lhs` -> `term_PR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PR_4_lhs";
    /// `rhs` -> `term_PR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PR_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Stage transition requires typed guard satisfaction.
pub mod pr_5 {
    /// `forAll` -> `term_PR_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PR_5_forAll";
    /// `lhs` -> `term_PR_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PR_5_lhs";
    /// `rhs` -> `term_PR_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PR_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Entry guard must be satisfied to enter a stage.
pub mod cg_1 {
    /// `forAll` -> `term_CG_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CG_1_forAll";
    /// `lhs` -> `term_CG_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CG_1_lhs";
    /// `rhs` -> `term_CG_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CG_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Exit guard must be satisfied, then the stage effect is applied.
pub mod cg_2 {
    /// `forAll` -> `term_CG_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_CG_2_forAll";
    /// `lhs` -> `term_CG_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_CG_2_lhs";
    /// `rhs` -> `term_CG_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_CG_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// The root resolver dispatch table is exhaustive and mutually exclusive over all TypeDefinitions.
pub mod dis_1 {
    /// `forAll` -> `term_DIS_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DIS_1_forAll";
    /// `lhs` -> `term_DIS_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DIS_1_lhs";
    /// `rhs` -> `term_DIS_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DIS_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Resolver dispatch is deterministic for every type.
pub mod dis_2 {
    /// `forAll` -> `term_DIS_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_DIS_2_forAll";
    /// `lhs` -> `term_DIS_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_DIS_2_lhs";
    /// `rhs` -> `term_DIS_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_DIS_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Disjoint parallel computations commute: A ⊗ B = B ⊗ A when site targets are disjoint.
pub mod par_1 {
    /// `forAll` -> `term_PAR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PAR_1_forAll";
    /// `lhs` -> `term_PAR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PAR_1_lhs";
    /// `rhs` -> `term_PAR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PAR_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Parallel free-count deltas are additive.
pub mod par_2 {
    /// `forAll` -> `term_PAR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PAR_2_forAll";
    /// `lhs` -> `term_PAR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PAR_2_lhs";
    /// `rhs` -> `term_PAR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PAR_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Partitioning is exhaustive: component cardinalities sum to total site budget.
pub mod par_3 {
    /// `forAll` -> `term_PAR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PAR_3_forAll";
    /// `lhs` -> `term_PAR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PAR_3_lhs";
    /// `rhs` -> `term_PAR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PAR_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// All interleavings of disjoint parallel computations yield the same final context.
pub mod par_4 {
    /// `forAll` -> `term_PAR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PAR_4_forAll";
    /// `lhs` -> `term_PAR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PAR_4_lhs";
    /// `rhs` -> `term_PAR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PAR_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Parallel certificate is the conjunction of component certificates plus disjointness.
pub mod par_5 {
    /// `forAll` -> `term_PAR_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_PAR_5_forAll";
    /// `lhs` -> `term_PAR_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_PAR_5_lhs";
    /// `rhs` -> `term_PAR_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_PAR_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// A ComputationDatum’s ring value is the content hash of its certificate.
pub mod ho_1 {
    /// `forAll` -> `term_HO_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HO_1_forAll";
    /// `lhs` -> `term_HO_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HO_1_lhs";
    /// `rhs` -> `term_HO_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HO_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Application preserves certification.
pub mod ho_2 {
    /// `forAll` -> `term_HO_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HO_2_forAll";
    /// `lhs` -> `term_HO_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HO_2_lhs";
    /// `rhs` -> `term_HO_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HO_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Composition certification requires both components certified and type-compatible.
pub mod ho_3 {
    /// `forAll` -> `term_HO_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HO_3_forAll";
    /// `lhs` -> `term_HO_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HO_3_lhs";
    /// `rhs` -> `term_HO_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HO_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Fully saturated partial application equals direct application.
pub mod ho_4 {
    /// `forAll` -> `term_HO_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_HO_4_forAll";
    /// `lhs` -> `term_HO_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_HO_4_lhs";
    /// `rhs` -> `term_HO_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_HO_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Every epoch terminates: the reduction within each epoch reaches convergence angle π.
pub mod str_1 {
    /// `forAll` -> `term_STR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_STR_1_forAll";
    /// `lhs` -> `term_STR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_STR_1_lhs";
    /// `rhs` -> `term_STR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_STR_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Grounding preservation across epoch boundaries.
pub mod str_2 {
    /// `forAll` -> `term_STR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_STR_2_forAll";
    /// `lhs` -> `term_STR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_STR_2_lhs";
    /// `rhs` -> `term_STR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_STR_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Every finite prefix computes in finite time.
pub mod str_3 {
    /// `forAll` -> `term_STR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_STR_3_forAll";
    /// `lhs` -> `term_STR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_STR_3_lhs";
    /// `rhs` -> `term_STR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_STR_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// The first epoch starts from the unfold seed context.
pub mod str_4 {
    /// `forAll` -> `term_STR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_STR_4_forAll";
    /// `lhs` -> `term_STR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_STR_4_lhs";
    /// `rhs` -> `term_STR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_STR_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Each subsequent epoch starts from the previous boundary’s continuation context.
pub mod str_5 {
    /// `forAll` -> `term_STR_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_STR_5_forAll";
    /// `lhs` -> `term_STR_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_STR_5_lhs";
    /// `rhs` -> `term_STR_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_STR_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Lease expiry at an epoch boundary returns claimed sites to the next epoch’s linear budget.
pub mod str_6 {
    /// `forAll` -> `term_STR_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_STR_6_forAll";
    /// `lhs` -> `term_STR_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_STR_6_lhs";
    /// `rhs` -> `term_STR_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_STR_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Every partial computation produces exactly one of Success or Failure.
pub mod flr_1 {
    /// `forAll` -> `term_FLR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FLR_1_forAll";
    /// `lhs` -> `term_FLR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FLR_1_lhs";
    /// `rhs` -> `term_FLR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FLR_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// A total computation always succeeds.
pub mod flr_2 {
    /// `forAll` -> `term_FLR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FLR_2_forAll";
    /// `lhs` -> `term_FLR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FLR_2_lhs";
    /// `rhs` -> `term_FLR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FLR_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Sequential failure propagation: if A fails, B is not evaluated.
pub mod flr_3 {
    /// `forAll` -> `term_FLR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FLR_3_forAll";
    /// `lhs` -> `term_FLR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FLR_3_lhs";
    /// `rhs` -> `term_FLR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FLR_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Parallel failure independence: one component’s failure does not prevent the other’s success.
pub mod flr_4 {
    /// `forAll` -> `term_FLR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FLR_4_forAll";
    /// `lhs` -> `term_FLR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FLR_4_lhs";
    /// `rhs` -> `term_FLR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FLR_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Recovery produces a new ComputationResult.
pub mod flr_5 {
    /// `forAll` -> `term_FLR_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FLR_5_forAll";
    /// `lhs` -> `term_FLR_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FLR_5_lhs";
    /// `rhs` -> `term_FLR_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FLR_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// The reduction’s existing rollback mechanism is a Recovery whose effect is the conjugate phase rotation.
pub mod flr_6 {
    /// `forAll` -> `term_FLR_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_FLR_6_forAll";
    /// `lhs` -> `term_FLR_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_FLR_6_lhs";
    /// `rhs` -> `term_FLR_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_FLR_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// In a linear trace, every site is targeted exactly once. Total effect count equals site budget.
pub mod ln_1 {
    /// `forAll` -> `term_LN_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LN_1_forAll";
    /// `lhs` -> `term_LN_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LN_1_lhs";
    /// `rhs` -> `term_LN_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LN_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// After a LinearEffect, the target site is pinned.
pub mod ln_2 {
    /// `forAll` -> `term_LN_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LN_2_forAll";
    /// `lhs` -> `term_LN_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LN_2_lhs";
    /// `rhs` -> `term_LN_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LN_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// A consumed LinearSite cannot be targeted again.
pub mod ln_3 {
    /// `forAll` -> `term_LN_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LN_3_forAll";
    /// `lhs` -> `term_LN_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LN_3_lhs";
    /// `rhs` -> `term_LN_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LN_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Lease allocation decrements the linear budget by the lease cardinality.
pub mod ln_4 {
    /// `forAll` -> `term_LN_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LN_4_forAll";
    /// `lhs` -> `term_LN_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LN_4_lhs";
    /// `rhs` -> `term_LN_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LN_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Lease expiry returns claimed sites to the budget.
pub mod ln_5 {
    /// `forAll` -> `term_LN_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LN_5_forAll";
    /// `lhs` -> `term_LN_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LN_5_lhs";
    /// `rhs` -> `term_LN_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LN_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Every geodesic trace is a linear trace.
pub mod ln_6 {
    /// `forAll` -> `term_LN_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_LN_6_forAll";
    /// `lhs` -> `term_LN_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_LN_6_lhs";
    /// `rhs` -> `term_LN_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_LN_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Subtyping is constraint superset: more constraints = more specific.
pub mod sb_1 {
    /// `forAll` -> `term_SB_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SB_1_forAll";
    /// `lhs` -> `term_SB_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SB_1_lhs";
    /// `rhs` -> `term_SB_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SB_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Subtype has fewer valid resolutions.
pub mod sb_2 {
    /// `forAll` -> `term_SB_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SB_2_forAll";
    /// `lhs` -> `term_SB_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SB_2_lhs";
    /// `rhs` -> `term_SB_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SB_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The constraint nerve of the supertype is a sub-complex of the subtype’s nerve.
pub mod sb_3 {
    /// `forAll` -> `term_SB_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SB_3_forAll";
    /// `lhs` -> `term_SB_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SB_3_lhs";
    /// `rhs` -> `term_SB_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SB_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// Covariance preserves inclusion.
pub mod sb_4 {
    /// `forAll` -> `term_SB_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SB_4_forAll";
    /// `lhs` -> `term_SB_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SB_4_lhs";
    /// `rhs` -> `term_SB_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SB_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Contravariance reverses inclusion.
pub mod sb_5 {
    /// `forAll` -> `term_SB_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SB_5_forAll";
    /// `lhs` -> `term_SB_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SB_5_lhs";
    /// `rhs` -> `term_SB_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SB_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Lattice depth equals site budget.
pub mod sb_6 {
    /// `forAll` -> `term_SB_6_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_SB_6_forAll";
    /// `lhs` -> `term_SB_6_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_SB_6_lhs";
    /// `rhs` -> `term_SB_6_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_SB_6_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Every recursive step strictly decreases the descent measure.
pub mod br_1 {
    /// `forAll` -> `term_BR_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BR_1_forAll";
    /// `lhs` -> `term_BR_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BR_1_lhs";
    /// `rhs` -> `term_BR_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BR_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Recursion depth is bounded by the initial measure value.
pub mod br_2 {
    /// `forAll` -> `term_BR_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BR_2_forAll";
    /// `lhs` -> `term_BR_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BR_2_lhs";
    /// `rhs` -> `term_BR_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BR_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Every bounded recursion terminates.
pub mod br_3 {
    /// `forAll` -> `term_BR_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BR_3_forAll";
    /// `lhs` -> `term_BR_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BR_3_lhs";
    /// `rhs` -> `term_BR_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BR_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Structural recursion’s measure is the input type’s structural size.
pub mod br_4 {
    /// `forAll` -> `term_BR_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BR_4_forAll";
    /// `lhs` -> `term_BR_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BR_4_lhs";
    /// `rhs` -> `term_BR_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BR_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The base predicate is satisfied exactly when the measure reaches zero.
pub mod br_5 {
    /// `forAll` -> `term_BR_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_BR_5_forAll";
    /// `lhs` -> `term_BR_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_BR_5_lhs";
    /// `rhs` -> `term_BR_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_BR_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// The working set is determined by the constraint nerve and the stage’s site targets.
pub mod rg_1 {
    /// `forAll` -> `term_RG_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RG_1_forAll";
    /// `lhs` -> `term_RG_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RG_1_lhs";
    /// `rhs` -> `term_RG_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RG_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Topological`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Topological";
}

/// All addresses within a region are within the region’s diameter under the chosen metric.
pub mod rg_2 {
    /// `forAll` -> `term_RG_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RG_2_forAll";
    /// `lhs` -> `term_RG_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RG_2_lhs";
    /// `rhs` -> `term_RG_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RG_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Total working set size is bounded by the addressable space at the quantum level.
pub mod rg_3 {
    /// `forAll` -> `term_RG_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RG_3_forAll";
    /// `lhs` -> `term_RG_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RG_3_lhs";
    /// `rhs` -> `term_RG_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RG_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// The resolver at stage k accesses only addresses within its working set.
pub mod rg_4 {
    /// `forAll` -> `term_RG_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_RG_4_forAll";
    /// `lhs` -> `term_RG_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_RG_4_lhs";
    /// `rhs` -> `term_RG_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_RG_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Ingested data conforms to the source’s declared type.
pub mod io_1 {
    /// `forAll` -> `term_IO_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IO_1_forAll";
    /// `lhs` -> `term_IO_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IO_1_lhs";
    /// `rhs` -> `term_IO_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IO_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Emitted data conforms to the sink’s declared type.
pub mod io_2 {
    /// `forAll` -> `term_IO_2_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IO_2_forAll";
    /// `lhs` -> `term_IO_2_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IO_2_lhs";
    /// `rhs` -> `term_IO_2_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IO_2_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Every ingestion through a source produces a valid ring datum via grounding.
pub mod io_3 {
    /// `forAll` -> `term_IO_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IO_3_forAll";
    /// `lhs` -> `term_IO_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IO_3_lhs";
    /// `rhs` -> `term_IO_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IO_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Every emission through a sink produces a valid surface symbol via projection.
pub mod io_4 {
    /// `forAll` -> `term_IO_4_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IO_4_forAll";
    /// `lhs` -> `term_IO_4_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IO_4_lhs";
    /// `rhs` -> `term_IO_4_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IO_4_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Pipeline`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Pipeline";
}

/// Every boundary effect touches at least one site.
pub mod io_5 {
    /// `forAll` -> `term_IO_5_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IO_5_forAll";
    /// `lhs` -> `term_IO_5_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IO_5_lhs";
    /// `rhs` -> `term_IO_5_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IO_5_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Inhabitance soundness (bidirectional). For any type:ConstrainedType T, cert:InhabitanceCertificate(T) .verified is true iff the carrier of T is non-empty. Discharge: the verdict reified by cert:InhabitanceCertificate agrees with the denotational carrier-non-emptiness predicate, by direct unfolding of cert:verified against the predicate semantics.
pub mod ih_1 {
    /// `forAll` -> `term_IH_1_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IH_1_forAll";
    /// `lhs` -> `term_IH_1_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IH_1_lhs";
    /// `rhs` -> `term_IH_1_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IH_1_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

/// Inhabitance cost (2-SAT restriction). For instances T satisfying predicate:Is2SatShape, the cost of resolver:TwoSatDecider on T is inherited from the classical 2-SAT decision procedure: O(n+m) where n is the variable count and m the clause count. Unrestricted IH_2 would be equivalent to P = NP and is not adopted.
pub mod ih_2a {
    /// `forAll` -> `term_IH_2a_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IH_2a_forAll";
    /// `lhs` -> `term_IH_2a_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IH_2a_lhs";
    /// `rhs` -> `term_IH_2a_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IH_2a_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Inhabitance cost (Horn-SAT restriction). For instances T satisfying predicate:IsHornShape, the cost of resolver:HornSatDecider on T is inherited from the classical Horn-SAT decision procedure via unit propagation: O(n+m).
pub mod ih_2b {
    /// `forAll` -> `term_IH_2b_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IH_2b_forAll";
    /// `lhs` -> `term_IH_2b_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IH_2b_lhs";
    /// `rhs` -> `term_IH_2b_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IH_2b_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Analytical`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Analytical";
}

/// Carrier preservation under basis reduction. The constraint-nerve reduction performed during inhabitance search preserves the carrier of the input ConstrainedType. Discharged against resolver:JacobianGuidedResolver and resolver:guidingJacobian vocabulary.
pub mod ih_3 {
    /// `forAll` -> `term_IH_3_forAll`
    pub const FOR_ALL: &str = "https://uor.foundation/schema/term_IH_3_forAll";
    /// `lhs` -> `term_IH_3_lhs`
    pub const LHS: &str = "https://uor.foundation/schema/term_IH_3_lhs";
    /// `rhs` -> `term_IH_3_rhs`
    pub const RHS: &str = "https://uor.foundation/schema/term_IH_3_rhs";
    /// `universallyValid`
    pub const UNIVERSALLY_VALID: bool = true;
    /// `validityKind` -> `Universal`
    pub const VALIDITY_KIND: &str = "https://uor.foundation/op/Universal";
    /// `verificationDomain` -> `Algebraic`
    pub const VERIFICATION_DOMAIN: &str = "https://uor.foundation/op/Algebraic";
}

use crate::enums::PrimitiveOp;

impl PrimitiveOp {
    /// Returns the arity of this operation (1 for unary, 2 for binary).
    #[must_use]
    pub const fn arity(self) -> i64 {
        match self {
            Self::Neg => 1,
            Self::Bnot => 1,
            Self::Succ => 1,
            Self::Pred => 1,
            Self::Add => 2,
            Self::Sub => 2,
            Self::Mul => 2,
            Self::Xor => 2,
            Self::And => 2,
            Self::Or => 2,
            Self::Le => 2,
            Self::Lt => 2,
            Self::Ge => 2,
            Self::Gt => 2,
            Self::Concat => 2,
            Self::Div => 2,
            Self::Mod => 2,
            Self::Pow => 2,
        }
    }

    /// Returns whether this operation is commutative.
    #[must_use]
    pub const fn is_commutative(self) -> bool {
        false
    }

    /// Returns whether this operation is an involution (self-inverse).
    #[must_use]
    pub const fn is_involution(self) -> bool {
        false
    }

    /// Returns the geometric character of this operation.
    #[must_use]
    pub const fn has_geometric_character(self) -> crate::enums::GeometricCharacter {
        match self {
            Self::Neg => crate::enums::GeometricCharacter::RingReflection,
            Self::Bnot => crate::enums::GeometricCharacter::HypercubeReflection,
            Self::Succ => crate::enums::GeometricCharacter::Rotation,
            Self::Pred => crate::enums::GeometricCharacter::RotationInverse,
            Self::Add => crate::enums::GeometricCharacter::Translation,
            Self::Sub => crate::enums::GeometricCharacter::Translation,
            Self::Mul => crate::enums::GeometricCharacter::Scaling,
            Self::Xor => crate::enums::GeometricCharacter::HypercubeTranslation,
            Self::And => crate::enums::GeometricCharacter::HypercubeProjection,
            Self::Or => crate::enums::GeometricCharacter::HypercubeJoin,
            Self::Le => crate::enums::GeometricCharacter::ConstraintSelection,
            Self::Lt => crate::enums::GeometricCharacter::ConstraintSelection,
            Self::Ge => crate::enums::GeometricCharacter::ConstraintSelection,
            Self::Gt => crate::enums::GeometricCharacter::ConstraintSelection,
            Self::Concat => crate::enums::GeometricCharacter::HypercubeJoin,
            Self::Div => crate::enums::GeometricCharacter::Quotient,
            Self::Mod => crate::enums::GeometricCharacter::Remainder,
            Self::Pow => crate::enums::GeometricCharacter::IteratedScaling,
        }
    }

    /// Returns true if this is a unary operation.
    #[must_use]
    pub const fn is_unary(self) -> bool {
        self.arity() == 1
    }

    /// Returns true if this is a binary operation.
    #[must_use]
    pub const fn is_binary(self) -> bool {
        self.arity() == 2
    }
}