UOR Euler Reduction

IRI: https://uor.foundation/reduction/
Prefix: reduction:
Space: kernel
Comment: Sequential composition of ψ-maps into a parameterized reduction ψ = ψ_9 ∘ … ∘ ψ_1. Defines stages, phase gates, rollback, and epochs.

Imports

https://uor.foundation/op/
https://uor.foundation/state/
https://uor.foundation/partition/
https://uor.foundation/resolver/
https://uor.foundation/morphism/
https://uor.foundation/observable/
https://uor.foundation/predicate/
https://uor.foundation/effect/
https://uor.foundation/schema/
https://uor.foundation/u/

Classes

Name	IRI	Subclass Of	Comment
EulerReduction	`https://uor.foundation/reduction/EulerReduction`	`http://www.w3.org/2002/07/owl#Thing`	The composite endofunctor ψ = ψ_9 ∘ … ∘ ψ_1, parameterized by Ω = e^{iπ/6}.
PhaseRotationScheduler	`https://uor.foundation/reduction/PhaseRotationScheduler`	`http://www.w3.org/2002/07/owl#Thing`	Schedule Ω⁰, Ω¹, …, Ω⁵ assigning a phase angle to each stage of the reduction.
TargetConvergenceAngle	`https://uor.foundation/reduction/TargetConvergenceAngle`	`http://www.w3.org/2002/07/owl#Thing`	The angle at which the reduction terminates (default: π).
PhaseGateAttestation	`https://uor.foundation/reduction/PhaseGateAttestation`	`http://www.w3.org/2002/07/owl#Thing`	Validation at each stage boundary checking that the accumulated phase angle matches the expected Ω^k.
ComplexConjugateRollback	`https://uor.foundation/reduction/ComplexConjugateRollback`	`http://www.w3.org/2002/07/owl#Thing`	Recovery operation when a phase gate fails: z → z̄. Involutory: applying twice yields the original value.
ReductionStep	`https://uor.foundation/reduction/ReductionStep`	`http://www.w3.org/2002/07/owl#Thing`	A named stage of the reduction. The standard reduction has six stages (Initialization through Convergence).
ReductionState	`https://uor.foundation/reduction/ReductionState`	`http://www.w3.org/2002/07/owl#Thing`	State of reduction execution at a specific point, including the current stage, phase angle, and pinned mask.
ReductionRule	`https://uor.foundation/reduction/ReductionRule`	`http://www.w3.org/2002/07/owl#Thing`	Guard-effect pair governing stage transitions in the reduction. The guard must be satisfied before the effect is applied.
Epoch	`https://uor.foundation/reduction/Epoch`	`http://www.w3.org/2002/07/owl#Thing`	Temporal segment of reduction execution. Each epoch represents one complete pass through the reduction stages.
EpochBoundary	`https://uor.foundation/reduction/EpochBoundary`	`http://www.w3.org/2002/07/owl#Thing`	Transition between epochs. Carries metadata about the epoch boundary crossing.
PredicateExpression	`https://uor.foundation/reduction/PredicateExpression`	`http://www.w3.org/2002/07/owl#Thing`	A Boolean expression over the reduction state. The atomic guard unit.
GuardExpression	`https://uor.foundation/reduction/GuardExpression`	`http://www.w3.org/2002/07/owl#Thing`	A conjunction of PredicateExpressions that must hold for a transition to fire.
TransitionEffect	`https://uor.foundation/reduction/TransitionEffect`	`http://www.w3.org/2002/07/owl#Thing`	State changes applied when a transition fires. Contains PropertyBind steps.
PropertyBind	`https://uor.foundation/reduction/PropertyBind`	`http://www.w3.org/2002/07/owl#Thing`	A single site pinning: target site + value.
ReductionAdvance	`https://uor.foundation/reduction/ReductionAdvance`	`http://www.w3.org/2002/07/owl#Thing`	Advancement from one ReductionStep to the next.
ServiceWindow	`https://uor.foundation/reduction/ServiceWindow`	`http://www.w3.org/2002/07/owl#Thing`	A sliding window over recent epochs providing BaseContext.
ReductionTransaction	`https://uor.foundation/reduction/ReductionTransaction`	`http://www.w3.org/2002/07/owl#Thing`	An atomic group of state changes within the reduction.
PipelineSuccess	`https://uor.foundation/reduction/PipelineSuccess`	`http://www.w3.org/2002/07/owl#Thing`	Successful termination (FullGrounding).
PipelineFailureReason	`https://uor.foundation/reduction/PipelineFailureReason`	`http://www.w3.org/2002/07/owl#Thing`	Typed failure: DispatchMiss, GroundingFailure, ConvergenceStall, etc.
PreflightCheck	`https://uor.foundation/reduction/PreflightCheck`	`http://www.w3.org/2002/07/owl#Thing`	A pre-execution validation: feasibility, dispatch coverage, coherence.
FeasibilityResult	`https://uor.foundation/reduction/FeasibilityResult`	`http://www.w3.org/2002/07/owl#Thing`	Result of a preflight check: feasibility witness or infeasibility witness.
LeaseState	`https://uor.foundation/reduction/LeaseState`	`http://www.w3.org/2002/07/owl#Thing`	Lifecycle of a partitioned context lease: Pending → Active → Released/Expired/Suspended.
ManagedLease	`https://uor.foundation/reduction/ManagedLease`	`http://www.w3.org/2002/07/owl#Thing`	A context lease with lifecycle tracking.
LeaseCheckpoint	`https://uor.foundation/reduction/LeaseCheckpoint`	`http://www.w3.org/2002/07/owl#Thing`	Snapshot of lease state at a point in time.
BackPressureSignal	`https://uor.foundation/reduction/BackPressureSignal`	`http://www.w3.org/2002/07/owl#Thing`	Flow control when reduction produces faster than downstream can consume.
DeferredQuerySet	`https://uor.foundation/reduction/DeferredQuerySet`	`http://www.w3.org/2002/07/owl#Thing`	Queries postponed to a future epoch.
SubleaseTransfer	`https://uor.foundation/reduction/SubleaseTransfer`	`http://www.w3.org/2002/07/owl#Thing`	Transfer of a lease from one computation to another.
ComparisonPredicate	`https://uor.foundation/reduction/ComparisonPredicate`	`https://uor.foundation/reduction/PredicateExpression`	Predicate comparing a state field against a value.
ConjunctionPredicate	`https://uor.foundation/reduction/ConjunctionPredicate`	`https://uor.foundation/reduction/PredicateExpression`	Conjunction (AND) of multiple predicates.
DisjunctionPredicate	`https://uor.foundation/reduction/DisjunctionPredicate`	`https://uor.foundation/reduction/PredicateExpression`	Disjunction (OR) of multiple predicates.
NegationPredicate	`https://uor.foundation/reduction/NegationPredicate`	`https://uor.foundation/reduction/PredicateExpression`	Negation (NOT) of a single predicate.
MembershipPredicate	`https://uor.foundation/reduction/MembershipPredicate`	`https://uor.foundation/reduction/PredicateExpression`	Predicate testing membership of an element in a set.
GroundingPredicate	`https://uor.foundation/reduction/GroundingPredicate`	`https://uor.foundation/reduction/PredicateExpression`	Predicate testing whether grounding exceeds a threshold.
SiteCoveragePredicate	`https://uor.foundation/reduction/SiteCoveragePredicate`	`https://uor.foundation/reduction/PredicateExpression`	Predicate testing whether a site coverage target is met.
EqualsPredicate	`https://uor.foundation/reduction/EqualsPredicate`	`https://uor.foundation/reduction/PredicateExpression`	Predicate testing equality of two expressions.
NonNullPredicate	`https://uor.foundation/reduction/NonNullPredicate`	`https://uor.foundation/reduction/PredicateExpression`	Predicate testing that a field is non-null.
QuerySubtypePredicate	`https://uor.foundation/reduction/QuerySubtypePredicate`	`https://uor.foundation/reduction/PredicateExpression`	Predicate testing whether a query is a subtype of a given type.
CompileUnit	`https://uor.foundation/reduction/CompileUnit`	`http://www.w3.org/2002/07/owl#Thing`	The typed input graph submitted to the reduction pipeline. Packages a root Term, target quantum level, verification domains, and thermodynamic budget. Stage 0 accepts exactly one CompileUnit and initializes the reduction state vector from it.

Properties

Name	Kind	Functional	Domain	Range	Comment
phaseParameter	Datatype	true	`https://uor.foundation/reduction/EulerReduction`	`http://www.w3.org/2001/XMLSchema#decimal`	The base phase parameter Ω for this reduction (e.g., e^{iπ/6}).
stageCount	Datatype	true	`https://uor.foundation/reduction/EulerReduction`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The number of stages in this reduction.
convergenceAngle	Datatype	true	`https://uor.foundation/reduction/EulerReduction`	`http://www.w3.org/2001/XMLSchema#decimal`	The cumulative phase angle at which the reduction converges.
composedOfMaps	Object	false	`https://uor.foundation/reduction/EulerReduction`	`https://uor.foundation/schema/TermExpression`	The ordered list of ψ-maps that compose this reduction.
rotationSchedule	Datatype	true	`https://uor.foundation/reduction/PhaseRotationScheduler`	`http://www.w3.org/2001/XMLSchema#decimal`	String representation of the rotation schedule Ω⁰, Ω¹, …, Ω⁵.
baseAngle	Datatype	true	`https://uor.foundation/reduction/PhaseRotationScheduler`	`http://www.w3.org/2001/XMLSchema#decimal`	The base angle π/6 from which the schedule is derived.
targetAngle	Datatype	true	`https://uor.foundation/reduction/TargetConvergenceAngle`	`http://www.w3.org/2001/XMLSchema#decimal`	The target convergence angle (default: π).
gateStage	Object	true	`https://uor.foundation/reduction/PhaseGateAttestation`	`https://uor.foundation/reduction/ReductionStep`	The reduction stage at which this gate is applied.
gateExpectedPhase	Datatype	true	`https://uor.foundation/reduction/PhaseGateAttestation`	`http://www.w3.org/2001/XMLSchema#decimal`	The expected phase angle Ω^k at this gate.
gateResult	Datatype	true	`https://uor.foundation/reduction/PhaseGateAttestation`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether the phase gate check passed or failed.
rollbackTarget	Object	true	`https://uor.foundation/reduction/ComplexConjugateRollback`	`https://uor.foundation/reduction/ReductionStep`	The reduction stage to which execution rolls back on gate failure.
stageIndex	Datatype	true	`https://uor.foundation/reduction/ReductionStep`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Zero-based index of this stage in the reduction.
stageName	Datatype	true	`https://uor.foundation/reduction/ReductionStep`	`http://www.w3.org/2001/XMLSchema#string`	Human-readable name of this reduction stage.
expectedPhase	Datatype	true	`https://uor.foundation/reduction/ReductionStep`	`http://www.w3.org/2001/XMLSchema#decimal`	The expected phase angle Ω^k at this stage.
entryGuard	Object	true	`https://uor.foundation/reduction/ReductionStep`	`https://uor.foundation/predicate/StatePredicate`	A typed predicate evaluated on the current ReductionState. Must be satisfied to enter this stage.
exitGuard	Object	true	`https://uor.foundation/reduction/ReductionStep`	`https://uor.foundation/predicate/StatePredicate`	A typed predicate that must be satisfied before the reduction advances past this stage.
stageEffect	Object	true	`https://uor.foundation/reduction/ReductionStep`	`https://uor.foundation/effect/Effect`	The effect applied by this stage upon successful exit.
currentStage	Object	true	`https://uor.foundation/reduction/ReductionState`	`https://uor.foundation/reduction/ReductionStep`	The reduction stage at which execution is currently positioned.
phaseAngle	Datatype	true	`https://uor.foundation/reduction/ReductionState`	`http://www.w3.org/2001/XMLSchema#decimal`	The accumulated phase angle at the current point.
pinnedMask	Datatype	true	`https://uor.foundation/reduction/ReductionState`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Bit mask of sites that are pinned (resolved) at this point.
freeRank	Datatype	true	`https://uor.foundation/reduction/ReductionState`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The number of free (unresolved) sites at this point.
transitionGuard	Object	true	`https://uor.foundation/reduction/ReductionRule`	`https://uor.foundation/predicate/GuardedTransition`	A typed GuardedTransition from predicate/ governing the stage transition.
transitionEffect	Object	true	`https://uor.foundation/reduction/ReductionRule`	`https://uor.foundation/schema/TermExpression`	The effect applied when this transition fires.
transitionAdvance	Datatype	true	`https://uor.foundation/reduction/ReductionRule`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether this transition advances to the next stage.
epochIndex	Datatype	true	`https://uor.foundation/reduction/Epoch`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Zero-based index of this epoch in the reduction execution.
epochDatum	Object	true	`https://uor.foundation/reduction/Epoch`	`https://uor.foundation/schema/TermExpression`	Metadata or summary datum for this epoch.
epochBoundaryType	Object	true	`https://uor.foundation/reduction/EpochBoundary`	`https://uor.foundation/schema/TermExpression`	The type of epoch boundary crossing (e.g., normal, forced, timeout).
predicateField	Datatype	true	`https://uor.foundation/reduction/PredicateExpression`	`http://www.w3.org/2001/XMLSchema#string`	The state field this predicate tests.
predicateOperator	Datatype	true	`https://uor.foundation/reduction/PredicateExpression`	`http://www.w3.org/2001/XMLSchema#string`	The comparison operator (e.g., '=', '<', '>=').
predicateValue	Datatype	true	`https://uor.foundation/reduction/PredicateExpression`	`http://www.w3.org/2001/XMLSchema#string`	The value against which the field is compared.
guardPredicates	Object	false	`https://uor.foundation/reduction/GuardExpression`	`https://uor.foundation/reduction/PredicateExpression`	The predicate expressions that compose this guard.
effectBindings	Object	false	`https://uor.foundation/reduction/TransitionEffect`	`https://uor.foundation/reduction/PropertyBind`	The property bind steps applied by this effect.
bindTarget	Datatype	true	`https://uor.foundation/reduction/PropertyBind`	`http://www.w3.org/2001/XMLSchema#string`	The target site identifier for this binding.
bindValue	Datatype	true	`https://uor.foundation/reduction/PropertyBind`	`http://www.w3.org/2001/XMLSchema#string`	The value to pin the target site to.
advanceFrom	Object	true	`https://uor.foundation/reduction/ReductionAdvance`	`https://uor.foundation/reduction/ReductionStep`	The source stage of the advancement.
advanceTo	Object	true	`https://uor.foundation/reduction/ReductionAdvance`	`https://uor.foundation/reduction/ReductionStep`	The target stage of the advancement.
windowSize	Datatype	true	`https://uor.foundation/reduction/ServiceWindow`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The number of recent epochs in this service window.
windowOffset	Datatype	true	`https://uor.foundation/reduction/ServiceWindow`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The starting epoch offset of this service window.
transactionPolicy	Datatype	true	`https://uor.foundation/reduction/ReductionTransaction`	`http://www.w3.org/2001/XMLSchema#string`	The execution policy for this transaction (e.g., AllOrNothing, BestEffort).
transactionOutcome	Object	true	`https://uor.foundation/reduction/ReductionTransaction`	`https://uor.foundation/schema/TermExpression`	The outcome of this transaction (e.g., committed, rolled back).
failureKind	Datatype	true	`https://uor.foundation/reduction/PipelineFailureReason`	`http://www.w3.org/2001/XMLSchema#string`	The kind of pipeline failure (e.g., DispatchMiss, ConvergenceStall).
preflightKind	Datatype	true	`https://uor.foundation/reduction/PreflightCheck`	`http://www.w3.org/2001/XMLSchema#string`	The kind of preflight check (e.g., feasibility, dispatch coverage).
preflightResult	Object	true	`https://uor.foundation/reduction/PreflightCheck`	`https://uor.foundation/schema/TermExpression`	The result of the preflight check (e.g., pass, fail).
groundingReached	Datatype	true	`https://uor.foundation/reduction/PipelineSuccess`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether full grounding was achieved.
feasibilityKind	Datatype	true	`https://uor.foundation/reduction/FeasibilityResult`	`http://www.w3.org/2001/XMLSchema#string`	The kind of feasibility result (e.g., Feasible, Infeasible).
feasibilityWitness	Datatype	true	`https://uor.foundation/reduction/FeasibilityResult`	`http://www.w3.org/2001/XMLSchema#string`	The witness justifying the feasibility or infeasibility result.
leasePhase	Datatype	true	`https://uor.foundation/reduction/LeaseState`	`http://www.w3.org/2001/XMLSchema#string`	The lifecycle phase of a lease (e.g., Pending, Active, Released).
managedLeaseId	Object	true	`https://uor.foundation/reduction/ManagedLease`	`https://uor.foundation/schema/TermExpression`	Unique identifier for this managed lease.
leaseLifecycle	Object	true	`https://uor.foundation/reduction/ManagedLease`	`https://uor.foundation/reduction/LeaseState`	The current lifecycle state of this managed lease.
checkpointEpoch	Datatype	true	`https://uor.foundation/reduction/LeaseCheckpoint`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The epoch index at which this checkpoint was taken.
checkpointState	Object	true	`https://uor.foundation/reduction/LeaseCheckpoint`	`https://uor.foundation/reduction/ReductionState`	The reduction state captured at this checkpoint.
pressureLevel	Datatype	true	`https://uor.foundation/reduction/BackPressureSignal`	`http://www.w3.org/2001/XMLSchema#string`	The current back-pressure level (e.g., Low, Medium, High).
pressureThreshold	Datatype	true	`https://uor.foundation/reduction/BackPressureSignal`	`http://www.w3.org/2001/XMLSchema#decimal`	The threshold at which back-pressure activates.
deferredCount	Datatype	true	`https://uor.foundation/reduction/DeferredQuerySet`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The number of queries in this deferred set.
deferralEpoch	Datatype	true	`https://uor.foundation/reduction/DeferredQuerySet`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The epoch in which these queries were deferred.
sourceLeaseRef	Object	true	`https://uor.foundation/reduction/SubleaseTransfer`	`https://uor.foundation/schema/TermExpression`	The lease being transferred from.
targetLeaseRef	Object	true	`https://uor.foundation/reduction/SubleaseTransfer`	`https://uor.foundation/schema/TermExpression`	The lease being transferred to.
transferredBudget	Datatype	true	`https://uor.foundation/reduction/SubleaseTransfer`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The site budget transferred between leases.
transferCompleted	Datatype	true	`https://uor.foundation/reduction/SubleaseTransfer`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether the sublease transfer has been completed.
comparisonField	Object	true	`https://uor.foundation/reduction/ComparisonPredicate`	`https://uor.foundation/schema/TermExpression`	The state field tested by this comparison predicate.
comparisonOperator	Object	true	`https://uor.foundation/reduction/ComparisonPredicate`	`https://uor.foundation/schema/TermExpression`	The comparison operator (e.g., '=', '<', '>=').
comparisonValue	Object	true	`https://uor.foundation/reduction/ComparisonPredicate`	`https://uor.foundation/schema/TermExpression`	The value against which the comparison is made.
conjuncts	Object	false	`https://uor.foundation/reduction/ConjunctionPredicate`	`https://uor.foundation/schema/TermExpression`	A conjunct predicate in a conjunction.
disjuncts	Object	false	`https://uor.foundation/reduction/DisjunctionPredicate`	`https://uor.foundation/schema/TermExpression`	A disjunct predicate in a disjunction.
negatedPredicate	Object	true	`https://uor.foundation/reduction/NegationPredicate`	`https://uor.foundation/schema/TermExpression`	The predicate being negated.
membershipSet	Object	true	`https://uor.foundation/reduction/MembershipPredicate`	`https://uor.foundation/schema/TermExpression`	The set against which membership is tested.
membershipElement	Object	true	`https://uor.foundation/reduction/MembershipPredicate`	`https://uor.foundation/schema/TermExpression`	The element being tested for set membership.
groundingThreshold	Datatype	true	`https://uor.foundation/reduction/GroundingPredicate`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The grounding threshold above which the predicate holds.
coverageTarget	Datatype	true	`https://uor.foundation/reduction/SiteCoveragePredicate`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The site coverage target expression.
equalityLeft	Object	true	`https://uor.foundation/reduction/EqualsPredicate`	`https://uor.foundation/schema/TermExpression`	The left-hand side of an equality test.
equalityRight	Object	true	`https://uor.foundation/reduction/EqualsPredicate`	`https://uor.foundation/schema/TermExpression`	The right-hand side of an equality test.
nonNullField	Datatype	true	`https://uor.foundation/reduction/NonNullPredicate`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The field that must be non-null.
queryTypeRef	Object	true	`https://uor.foundation/reduction/QuerySubtypePredicate`	`https://uor.foundation/schema/TermExpression`	The query type reference for subtype testing.
siteState	Object	true	`https://uor.foundation/reduction/ReductionState`	`https://uor.foundation/schema/TermExpression`	The site state descriptor within a reduction state.
transactionScope	Object	true	`https://uor.foundation/reduction/ReductionTransaction`	`https://uor.foundation/schema/TermExpression`	The scope of sites affected by this transaction.
transactionStatus	Object	true	`https://uor.foundation/reduction/ReductionTransaction`	`https://uor.foundation/schema/TermExpression`	Current status of this transaction (e.g., pending, committed).
baseContextRef	Object	true	`https://uor.foundation/reduction/ServiceWindow`	`https://uor.foundation/schema/TermExpression`	Reference to the base context provided by this service window.
leaseRemainingBudget	Datatype	true	`https://uor.foundation/reduction/LeaseCheckpoint`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The remaining site budget at this checkpoint.
expiryEpoch	Datatype	true	`https://uor.foundation/reduction/ManagedLease`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The epoch at which this managed lease expires.
leaseBudget	Datatype	true	`https://uor.foundation/reduction/ManagedLease`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The total site budget allocated to this managed lease.
sourceStage	Object	true	`https://uor.foundation/reduction/BackPressureSignal`	`https://uor.foundation/schema/TermExpression`	The source stage emitting back-pressure.
targetStage	Object	true	`https://uor.foundation/reduction/BackPressureSignal`	`https://uor.foundation/schema/TermExpression`	The target stage receiving back-pressure.
deferralReason	Object	true	`https://uor.foundation/reduction/DeferredQuerySet`	`https://uor.foundation/schema/TermExpression`	The reason for deferring these queries.
infeasibilityKind	Object	true	`https://uor.foundation/reduction/FeasibilityResult`	`https://uor.foundation/schema/TermExpression`	The kind of infeasibility detected.
failureStage	Object	true	`https://uor.foundation/reduction/PipelineFailureReason`	`https://uor.foundation/schema/TermExpression`	The reduction stage at which the pipeline failure occurred.
finalGrounding	Datatype	true	`https://uor.foundation/reduction/PipelineSuccess`	`http://www.w3.org/2001/XMLSchema#decimal`	The final grounding level achieved on pipeline success.
preservedGrounding	Datatype	true	`https://uor.foundation/reduction/EpochBoundary`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether grounding was preserved across the epoch boundary.
rootTerm	Object	true	`https://uor.foundation/reduction/CompileUnit`	`https://uor.foundation/schema/TermExpression`	The root term expression of a CompileUnit — the top-level syntactic node from which all sub-expressions descend.
unitWittLevel	Object	true	`https://uor.foundation/reduction/CompileUnit`	`https://uor.foundation/schema/WittLevel`	The quantum level at which this CompileUnit operates.
thermodynamicBudget	Datatype	true	`https://uor.foundation/reduction/CompileUnit`	`http://www.w3.org/2001/XMLSchema#decimal`	The Landauer-bounded energy budget for this CompileUnit's resolution, measured in k_B T ln 2 units.
targetDomains	Object	false	`https://uor.foundation/reduction/CompileUnit`	`https://uor.foundation/op/VerificationDomain`	The verification domain(s) targeted by this CompileUnit.
unitAddress	Object	true	`https://uor.foundation/reduction/CompileUnit`	`https://uor.foundation/u/Element`	Content-addressable identifier computed as the u:Element of the root term’s transitive closure. Computed by stage_initialization, not declared by the submitter. Excludes budget, domains, and quantum level to enable memoization.
preflightOrder	Datatype	true	`https://uor.foundation/reduction/PreflightCheck`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Zero-based execution order for preflight checks. Lower indices execute first. BudgetSolvencyCheck (order 0) must precede all others.

Named Individuals

Name	Type	Properties	Comment
Initialization	`https://uor.foundation/reduction/ReductionStep`	`stageIndex`: 0 `stageName`: Initialization `expectedPhase`: Ω⁰	Stage 0: initialize state vector to identity.
Declare	`https://uor.foundation/reduction/ReductionStep`	`stageIndex`: 1 `stageName`: Declare `expectedPhase`: Ω¹	Stage 1: dispatch resolver (δ selects).
Factorize	`https://uor.foundation/reduction/ReductionStep`	`stageIndex`: 2 `stageName`: Factorize `expectedPhase`: Ω²	Stage 2: produce valid ring address (G grounds).
Resolve	`https://uor.foundation/reduction/ReductionStep`	`stageIndex`: 3 `stageName`: Resolve `expectedPhase`: Ω³	Stage 3: resolve constraints (Π terminates).
Attest	`https://uor.foundation/reduction/ReductionStep`	`stageIndex`: 4 `stageName`: Attest `expectedPhase`: Ω⁴	Stage 4: accumulate without contradiction (α consistent).
Extract	`https://uor.foundation/reduction/ReductionStep`	`stageIndex`: 5 `stageName`: Extract `expectedPhase`: Ω⁵	Stage 5: extract coherent output (P projects).
Convergence	`https://uor.foundation/reduction/ReductionStep`	`stageIndex`: 6 `stageName`: Convergence `expectedPhase`: π	Terminal stage: reduction has reached the convergence angle π.
gate_initialization	`https://uor.foundation/reduction/PhaseGateAttestation`	`gateStage`: `https://uor.foundation/reduction/stage_initialization` `gateExpectedPhase`: Ω⁰ `gateResult`: true	Phase gate at stage 0 boundary: checks Ω⁰ = 1.
gate_declare	`https://uor.foundation/reduction/PhaseGateAttestation`	`gateStage`: `https://uor.foundation/reduction/stage_declare` `gateExpectedPhase`: Ω¹ `gateResult`: true	Phase gate at stage 1 boundary: checks Ω¹.
gate_factorize	`https://uor.foundation/reduction/PhaseGateAttestation`	`gateStage`: `https://uor.foundation/reduction/stage_factorize` `gateExpectedPhase`: Ω² `gateResult`: true	Phase gate at stage 2 boundary: checks Ω².
gate_resolve	`https://uor.foundation/reduction/PhaseGateAttestation`	`gateStage`: `https://uor.foundation/reduction/stage_resolve` `gateExpectedPhase`: Ω³ `gateResult`: true	Phase gate at stage 3 boundary: checks Ω³.
gate_attest	`https://uor.foundation/reduction/PhaseGateAttestation`	`gateStage`: `https://uor.foundation/reduction/stage_attest` `gateExpectedPhase`: Ω⁴ `gateResult`: true	Phase gate at stage 4 boundary: checks Ω⁴.
gate_extract	`https://uor.foundation/reduction/PhaseGateAttestation`	`gateStage`: `https://uor.foundation/reduction/stage_extract` `gateExpectedPhase`: Ω⁵ `gateResult`: true	Phase gate at stage 5 boundary: checks Ω⁵.
euler_reduction_instance	`https://uor.foundation/reduction/EulerReduction`	`phaseParameter`: e^{iπ/6} `stageCount`: 6 `convergenceAngle`: π	The canonical Euler reduction instance with Ω = e^{iπ/6} and 6 stages.
phase_schedule	`https://uor.foundation/reduction/PhaseRotationScheduler`	`rotationSchedule`: Ω⁰, Ω¹, Ω², Ω³, Ω⁴, Ω⁵ `baseAngle`: π/6	The canonical phase rotation schedule for the 6-stage reduction.
convergence_target	`https://uor.foundation/reduction/TargetConvergenceAngle`	`targetAngle`: π	The default convergence target angle π.
conjugate_rollback	`https://uor.foundation/reduction/ComplexConjugateRollback`	`rollbackTarget`: `https://uor.foundation/reduction/stage_initialization`	The canonical complex conjugate rollback operation: z → z̄.
DispatchMiss	`https://uor.foundation/reduction/PipelineFailureReason`	`failureKind`: DispatchMiss	Failure: no resolver matched the dispatch query.
GroundingFailure	`https://uor.foundation/reduction/PipelineFailureReason`	`failureKind`: GroundingFailure	Failure: grounding to a valid ring address failed.
ConvergenceStall	`https://uor.foundation/reduction/PipelineFailureReason`	`failureKind`: ConvergenceStall	Failure: reduction stalled before reaching convergence angle.
ContradictionDetected	`https://uor.foundation/reduction/PipelineFailureReason`	`failureKind`: ContradictionDetected	Failure: accumulation detected a logical contradiction.
CoherenceViolation	`https://uor.foundation/reduction/PipelineFailureReason`	`failureKind`: CoherenceViolation	Failure: coherence constraint violated during extraction.
FullGroundingSuccess	`https://uor.foundation/reduction/PipelineSuccess`	`groundingReached`: true	Successful termination: all sites saturated.
FeasibilityCheck	`https://uor.foundation/reduction/PreflightCheck`	`preflightKind`: Feasibility `preflightOrder`: 1	Preflight: checks that the reduction can reach convergence.
DispatchCoverageCheck	`https://uor.foundation/reduction/PreflightCheck`	`preflightKind`: DispatchCoverage `preflightOrder`: 2	Preflight: checks that every dispatch query has a resolver.
PackageCoherenceCheck	`https://uor.foundation/reduction/PreflightCheck`	`preflightKind`: PackageCoherence `preflightOrder`: 3	Preflight: checks package-level coherence constraints.
default_service_window	`https://uor.foundation/reduction/ServiceWindow`	`windowSize`: 3 `windowOffset`: 0	The default service window: 3 epochs, zero offset.
advance_init_to_declare	`https://uor.foundation/reduction/ReductionAdvance`	`advanceFrom`: `https://uor.foundation/reduction/stage_initialization` `advanceTo`: `https://uor.foundation/reduction/stage_declare`	Advancement from Initialization to Declare.
atomic_transaction	`https://uor.foundation/reduction/ReductionTransaction`	`transactionPolicy`: AllOrNothing	An all-or-nothing atomic reduction transaction.
empty_guard	`https://uor.foundation/reduction/GuardExpression`	—	A trivially satisfied guard with no predicates.
identity_effect	`https://uor.foundation/reduction/TransitionEffect`	—	The identity effect: no state changes.
true_predicate	`https://uor.foundation/reduction/PredicateExpression`	`predicateField`: * `predicateOperator`: true `predicateValue`: *	A predicate that always evaluates to true.
noop_bind	`https://uor.foundation/reduction/PropertyBind`	`bindTarget`: none `bindValue`: unchanged	A no-op property binding that changes nothing.
Pending	`https://uor.foundation/reduction/LeaseState`	`leasePhase`: Pending	Lease is pending activation.
Active	`https://uor.foundation/reduction/LeaseState`	`leasePhase`: Active	Lease is active and resources are allocated.
Released	`https://uor.foundation/reduction/LeaseState`	`leasePhase`: Released	Lease has been explicitly released.
Expired	`https://uor.foundation/reduction/LeaseState`	`leasePhase`: Expired	Lease has expired due to timeout.
Suspended	`https://uor.foundation/reduction/LeaseState`	`leasePhase`: Suspended	Lease is temporarily suspended.
FeasibilityWitness	`https://uor.foundation/reduction/FeasibilityResult`	`feasibilityKind`: Feasible	Preflight result: reduction is feasible.
InfeasibilityWitness	`https://uor.foundation/reduction/FeasibilityResult`	`feasibilityKind`: Infeasible `feasibilityWitness`: obstruction detected	Preflight result: reduction is infeasible.
PreflightTiming	`https://uor.foundation/reduction/PreflightCheck`	`preflightKind`: Timing `preflightOrder`: 4	Preflight: timing feasibility check.
RuntimeTiming	`https://uor.foundation/reduction/PreflightCheck`	`preflightKind`: RuntimeTiming `preflightOrder`: 5	Preflight: runtime timing bounds check.
BudgetSolvencyCheck	`https://uor.foundation/reduction/PreflightCheck`	`preflightKind`: BudgetSolvency `preflightOrder`: 0	Preflight: verifies thermodynamicBudget ≥ bitsWidth(unitWittLevel) × ln 2. Rejects the CompileUnit if the budget is absent or insufficient. Must execute before all other preflights (preflightOrder 0). Cost is O(1) per CS_4.
BackPressureDefault	`https://uor.foundation/reduction/BackPressureSignal`	`pressureLevel`: Medium `pressureThreshold`: 0.75	Default back-pressure signal with medium threshold.