Glossary: U

Definitions in this project whose names start with U. The whole glossary has the other sections.

A · B · C · D · E · F · G · H · I · J · K · L · M · N · O · P · Q · R · S · T · U · V · W · X · Y · Z · Other

U def

The block space U_A, as an actual binary submodule. Membership uses y + Q a because subtraction equals addition in characteristic two. · OAI.MaxCutGames.Quadratic.U

U def

The common-denominator-cleared regular matrices used in exact arithmetic. · OAI.RationalHitting.Generator.U

U def

The block space U_A, as an actual binary submodule. Membership uses y + Q a because subtraction equals addition in characteristic two. · OAI.UniqueGamesTheorem.Quadratic.U

u def

Cheap row-advancing vector. · OAI.TreeEdit.BinaryLower.FiniteVectors.u

ud def

upward round division · OAI.GeneralMahler.Cert.IV.ud

uGradeEquiv def

The induced U-graded space is the subspace of the old grade. · OAI.IntegralCharacterVarieties.IntrinsicInterval.Data.uGradeEquiv

uLayers def

The finite set of the U layers. · OAI.Problem335.BalancedSchedule.uLayers

Ultra structure

Family of orientation/flag-conditional laws (μ already realizes joint flag law). · OAI.HadwigerCounterexample.Ultra

UltraCompletion abbrev

The actual Banach completion of the normed ultralimit quotient. · OAI.Tingley.UltraCompletion

ultraCon def

The ring congruence defining the norm (not algebraic) ultrapower. · OAI.NuclearUltrapower.ultraCon

ultranorm def

The actual ultralimit of coordinate norms. · OAI.Tingley.UltraSequence.ultranorm

UltraPreHilbert def

A type synonym for bounded Hilbert families, equipped below with the ultralimit semi-inner-product (not with the supremum norm). · OAI.NuclearUltrapower.UltraPreHilbert

UltraQuotient abbrev

The normed space obtained by identifying sequences at zero ultradistance. · OAI.Tingley.UltraQuotient

ultraRel def

Equality modulo I_omega(B). This is equivalent to norm-null difference. · OAI.NuclearUltrapower.ultraRel

UltraSequence structure

A fresh carrier on which only the ultralimit topology will be installed. · OAI.Tingley.UltraSequence

ultraSphereEquiv def

Surjectivity comes from the actual coordinatewise inverse, not from isometry alone. · OAI.Tingley.ultraSphereEquiv

ultraweakTopology def

The actual ultraweak topology, generated by absolutely summable vector functionals. No continuity of a chosen trace is built into this definition. · OAI.FiniteFactor.ultraweakTopology

ultraweakTopology abbrev

The ultraweak topology is generated by absolutely summable vector functionals. · OAI.RelativeGeneration.ultraweakTopology

ultraweakTopology def

The actual ultraweak topology, generated by absolutely summable vector functionals. No continuity of a chosen trace is built into this definition. · OAI.UltrapowerBridge.ultraweakTopology

UMap structure

A smooth ambient representative of a smooth unitary-valued map. · OAI.KervaireUnitaryHomotopy.UMap

unary def

One literal unary stretch; it samples one transition from the original kernel tower rather than introducing independent or replacement disorder. · OAI.DilutedSpinGlass.PrescribedTree.unary

unaryBlockMapAt def

A fixed table lookup or fixed pattern permutation can follow immediately after the physical unary decoding, with one genuine finite TM2 transition. · OAI.MaxCutGames.Foundations.Complexity.FinalCNFMachine.unaryBlockMapAt

unaryBlockMapAt def

A fixed table lookup or fixed pattern permutation can follow immediately after the physical unary decoding, with one genuine finite TM2 transition. · OAI.UniqueGamesTheorem.Foundations.Complexity.FinalCNFMachine.unaryBlockMapAt

unaryCode def

Unary loop count. These symbols are explicitly popped by the loop body. · OAI.RationalHitting.StackLanguage.unaryCode

unaryInput def

A fixed three-stack parser for the literal, unescaped unary input. Its output is the ordinary typed pair coding used by the closure library. · OAI.RationalHitting.StackLanguage.Procedure.unaryInput

unaryLength def

Consume a word, emitting its unary length, independently of its bits. · OAI.RationalHitting.StackLanguage.unaryLength

UnaryRelation structure

An equality-invariant regular forcing predicate, used only to produce bounded HS subnames by literal collection. · OAI.PartitionConsistency.SetForcingNames.SymmetricSystem.UnaryRelation

unaryScanBody def

Strip the one literal separator of the required unary input, remembering its first field in a separate finite stack. · OAI.RationalHitting.StackLanguage.unaryScanBody

UnarySegmentPartition structure

A finite partition of a unary run into its actual successive segments. · OAI.LipschitzHilbert.UnarySegmentPartition

unaryTapes def

A caller's tape frame with the two unary prefixes and their unread suffixes. · OAI.MaxCutGames.Foundations.Complexity.MachineUnaryAddAt.unaryTapes

unaryTapes def

A caller's tape frame with the two unary prefixes and their unread suffixes. · OAI.UniqueGamesTheorem.Foundations.Complexity.MachineUnaryAddAt.unaryTapes

unaryToBits def

Unary-to-binary conversion charges every carry and all word moves. · OAI.ExactQuantumFactoring.BitStackProgram.Procedure.unaryToBits

unaryWord def

A fixed finite stack program with literal unary input and exact canonical output, bounded by a fixed polynomial in the input length. · OAI.RationalHitting.ExecutableGenerator.unaryWord

Unbinned def

The unbinned event quantifies no artificial stage data: the bin witness is forced by the literal label words. · OAI.TorsionFreeZeroDivisors.ActualPatternEvent.Unbinned

UnboundedStep inductive

Unbounded left-ended tape semantics. A cell beyond the finite represented region is blank; it is materialized only when reached. No output fact or acceptance relation is built into these transition constructors. · OAI.FiniteAlgebraicEnvelopes.Compiler.Simulator.UnboundedStep

uncenteredIntrinsicProduct def

The intrinsic product transported from the sampled point to the uncentered time coordinates of the box. · OAI.DukePrimeDegree.RootPrefixBox.uncenteredIntrinsicProduct

uncurry def

Uncurrying preserves positivity, augmentation, and the signed differential. · OAI.Thomason.Construction.DirectedComplex.RightPath.uncurry

uncurryLoop def

Uncurry the first path coordinate into a based cube. · OAI.Thomason.Construction.HomotopyMaps.uncurryLoop

uncurryLoopHomotopy def

Conversely a path-space cubical homotopy uncurries relative to the full boundary. · OAI.Thomason.Construction.HomotopyMaps.uncurryLoopHomotopy

under def

True precisely on a vertex's descendants (including the vertex itself). · OAI.KServer.Rounding.Tree.under

underlyingCategory def

Recovering objects and 1-cells is functorial in strict omega-categories. · OAI.Thomason.Construction.StrictOmegaCategory.underlyingCategory

underlyingComparison def

The comparison is natural, retaining the actual underlying maps and differentials. · OAI.LittleFinitistic.BimoduleBalancedTensor.underlyingComparison

underlyingComparison def

The comparison preserves the original maps in the arbitrary input complex. · OAI.LittleFinitistic.BimoduleTotal.underlyingComparison

underlyingComplex abbrev

Forgetting to k uses the actual restriction-of-scalars functor on complexes. · OAI.LittleFinitistic.OrdinarySimulation.underlyingComplex

underlyingEquiv def

Forgetting the actual left B action gives exactly the original balanced tensor vector space. · OAI.LittleFinitistic.BimoduleBalancedTensor.underlyingEquiv

underlyingGraph def

The underlying simple graph used in the planar-separator argument. Its adjacency is induced by real edge copies of the rotation system. · OAI.HyperbolicObstruction.PictureSwitch.PictureMap.underlyingGraph

underlyingIso def

Forgetting the full left action recovers the frozen signed tensor total with its actual differential. · OAI.LittleFinitistic.BimoduleTotal.underlyingIso

underlyingRightComplex abbrev

The actual underlying right-B complex of the genuine dg bimodule. · OAI.LittleFinitistic.OrdinarySimulation.underlyingRightComplex

understand def

The (fixed) program is specialized to a maximum length. · OAI.Fifths.SM.understand

undoLocal def

Reconstruct the preceding control and read symbol from the new control and the complete symbol that was written. No checkpoint invariant is consulted. · OAI.ForcedComputation.Recorder.undoLocal

unequalEdges def

Precisely the selected unequal-original-label edges of a matching. · OAI.TreeEdit.BinaryLower.Code.unequalEdges

unfill def

Recover the relative path homotopy from a genuine square having the specified four boundary sides. · OAI.HyperbolicObstruction.SquarePathFilling.unfill

unfolded def

Restore the removed alphabet component of the affine intercept. · OAI.MaxCutGames.Decoder.TableKeysGame.unfolded

unfolded def

Restore the removed alphabet component of the affine intercept. · OAI.UniqueGamesTheorem.Decoder.TableKeysGame.unfolded

unfoldedModeDensity def

The actual unfolded spectral density of a retained angular mode, of mass q da. The argument q₀ is its zero-extended representative in the jitter good arc. · OAI.ThreeTorus.unfoldedModeDensity

unfoldedVertex def

Finite unfolding places every vertex in the countable reflection orbit. · OAI.TriangularBilliards.unfoldedVertex

unframe def

Frames are invertible (so cancellation along a path suffices). · OAI.PowerSaving.Binary.unframe

Uniform def

A single finite-alphabet classical generator receives only the INPUT LENGTH. All stack alphabets, states and labels are finite: no large-integer unit-cost oracle is hidden in TM2 push/branch functions. · OAI.ExactQuantumFactoring.Uniform

Uniform structure

The exact three uniform finite-bound assertions, expressed without identifying dependent candidate/value indices by extra axioms. · OAI.PureTypeSystem.ObservationValues.Uniform

uniform def

Uniform probability, not counting measure. · OAI.CoordinateSweeps.FiniteLaw.uniform

uniform def

Uniform V constructor. Q binds w:Single(z-down), then z:Z. · OAI.PureTypeSystem.Labelled.ProbeCode.uniform

uniform def

The genuine partition into all depth-n dyadic cells. · OAI.ThompsonNonamenability.BasicPartition.uniform

UniformAffineApproximation def

The uniform conclusion needed from the arbitrary-tolerance affine lemma. Slopes are fixed before h is chosen, and every minimizing branch, including ties, must approximate. · OAI.Problem326.BarrierConstruction.UniformAffineApproximation

UniformAlgorithmClaim def

Full uniform main objective in the explicit bit model, not a theorem or assumption. Machine transition steps are bit operations. Installing the standard input and reading/erasing the output adds only O(L + budget) charged bit operations, … · OAI.UniformKServer.UniformAlgorithmClaim

UniformApproximation def

The approximation list may contain functions outside the column hull. · OAI.MetricEntropyDuality.UniformApproximation

uniformArrivalLaw def

Uniform random arrival order, including the unique order on the empty ground set. · OAI.MatroidProphet.Secretary.uniformArrivalLaw

uniformAverage def

The normalized uniform sum on a concrete finite outcome space. · OAI.MaxCutGames.Soundness.RepeatedGameBounds.uniformAverage

uniformAverage def

The normalized uniform sum on a concrete finite outcome space. · OAI.UniqueGamesTheorem.Soundness.RepeatedGameBounds.uniformAverage

UniformAveragingGap def

The precise uniform operator consequence of the Kazhdan estimate for the chosen generators, on the coefficient Hilbert space used by the Roe module. For the standard generators this is the specialization of BHV, Proposition 1.3.2 and … · OAI.CoarseAssembly.UniformAveragingGap

uniformCell def

The cell with index k in the depth-n uniform dyadic partition. · OAI.ThompsonNonamenability.BasicPartition.uniformCell

uniformCells def

All cells at depth n, with no repeated intervals. · OAI.ThompsonNonamenability.BasicPartition.uniformCells

uniformChiSquare def

Pearson divergence against the uniform law, written with its constant denominator cleared. uniformChiSquare_eq_pearson identifies the actual likelihood-ratio definition. · OAI.MaxCutGames.Decoder.SparseLaw.uniformChiSquare

uniformChiSquare def

Pearson divergence against the uniform law, written with its constant denominator cleared. uniformChiSquare_eq_pearson identifies the actual likelihood-ratio definition. · OAI.UniqueGamesTheorem.Decoder.SparseLaw.uniformChiSquare

UniformCommutatorEstimate def

The exact universal quantifiers of Theorem thm:universal. · OAI.KadisonSimilarity.UniformCommutatorEstimate

uniformCount def

The number of first-system intervals: exactly 1 / Hx. · OAI.QuantitativeVanDerWaerden.ConstructionModel.uniformCount

UniformDyadicPLWitness structure

A genuine affine formula on every closed cell of one uniform subdivision. · OAI.ThompsonNonamenability.UniformDyadicPLWitness

uniformDyadicPoint def

A point on the closed depth-n dyadic grid, including both endpoints. · OAI.ThompsonNonamenability.uniformDyadicPoint

UniformEmbeddings def

Uniform distortion means one finite constant, with a separate map and a separate positive scale for each depth. · OAI.DiamondDistortion.Diamond.UniformEmbeddings

UniformFactorStability def

Factor stability with a tolerance independent of the represented factors. Zero-dimensional representations are allowed. · OAI.KadisonKastler.UniformFactorStability

uniformFamily def

Choose norm-controlled representatives of a bounded operator-field family. · OAI.KadisonKastler.WeakOperatorField.uniformFamily

uniformGapCells def

Consecutive cells with indices A, ..., A+c-1 on grid level n. · OAI.ThompsonNonamenability.uniformGapCells

UniformGerm structure

Uniform complex neighborhood of the actual normalized sonic equation. The parameter-to-germ map is constructed, not postulated as a shooting input. · OAI.SepticProfile.SourceFamily.UniformGerm

uniformInterval def

Normalized Lebesgue measure on a half-open interval of positive length. · OAI.WeakPinned.Grid.uniformInterval

uniformizer def

The actual ramified parameter in the cyclotomic quotient. · OAI.CirculantHadamard.RamifiedLocal.uniformizer

uniformLaw def

The inherited product-law realization, not a fresh informal conditioning. · OAI.FKCRT.SimpleWalk.uniformLaw

UniformLocalCATZero def

A uniform ambient neighborhood lies in a CAT(0) subspace. · OAI.HyperbolicObstruction.UniformLocalCATZero

UniformLocalization def

The uniform estimate, with the eventual quantifier outside all circuit data. · OAI.QAC.UniformLocalization

uniformLogWeights_compactParameter def

Only compactness of the parameter range, joint smoothness and common support are needed; no Mellin estimate is assumed. · OAI.CubicFirstMoment.uniformLogWeights_compactParameter

uniformLogWeights_constant def

A fixed test function, with any index set, has the required uniform support and derivative bounds. · OAI.CubicFirstMoment.uniformLogWeights_constant

UniformlyNonpretentious def

Uniform nonpretentiousness against every fixed Dirichlet character. · OAI.TwoPointCorrelations.UniformlyNonpretentious

UniformMargin def

A uniformly strict bound on all missed costs. This is an equivalent, convenient form of the supremum margin for a strict comparison. · OAI.PartitionConsistency.DiagramOrder.UniformMargin

uniformMarginal def

Marginal of the uniform distribution on ι along an actual line map. · OAI.RowColumn.uniformMarginal

uniformMass def

The uniform mass on a nonempty finite space. · OAI.ContingencyTables.ResidualMixture.uniformMass

uniformMean def

Uniform expectation, implemented by its normalized finite sum. · OAI.MaxCutGames.Soundness.SubsetIntersection.uniformMean

uniformMean def

Uniform weak-composition mean of an actual natural-valued function. · OAI.Problem335.FactorialExpansion.uniformMean

uniformMean def

Expectation under the uniform law on a finite type. · OAI.SidorenkoCounterexample.uniformMean

uniformMean def

Uniform expectation, implemented by its normalized finite sum. · OAI.UniqueGamesTheorem.Soundness.SubsetIntersection.uniformMean

UniformMeasurableOperators structure

The exact uniformly bounded measurable family needed for coefficient averaging. The bound is retained as data to control the output operator. · OAI.KadisonKastler.UniformMeasurableOperators

uniformMeasure def

The formalization proves one-third Hölder stability of Brenier maps from the uniform measure on a compact convex body with nonempty interior in $\mathbb R^d$, for every $d\ge2$. For targets supported in one fixed nonempty compact set, the … · OAI.Problem358.uniformMeasure

UniformMixedBound def

All mixed small-component slices of total degree at most r, with their exact ambient normalization weight. No Hybrid derivative bound is included in this property. Fixed primal points and prescribed frequencies are arbitrary. · OAI.MaxCutGames.Inverse.KMSAnalyticHybridEnergy.UniformMixedBound

UniformMixedBound def

All mixed small-component slices of total degree at most r, with their exact ambient normalization weight. No Hybrid derivative bound is included in this property. Fixed primal points and prescribed frequencies are arbitrary. · OAI.UniqueGamesTheorem.Inverse.KMSAnalyticHybridEnergy.UniformMixedBound

uniformNoise def

The actual operator samples both rank-one factors uniformly, including zero. · OAI.MaxCutGames.Inverse.KMSLowLevel.uniformNoise

uniformNoise def

The actual operator samples both rank-one factors uniformly, including zero. · OAI.UniqueGamesTheorem.Inverse.KMSLowLevel.uniformNoise

uniformOfRefines def

Restricting an original affine piece to a contained grid cell preserves its exact exponent; the translation is rebased at the new left endpoint. · OAI.ThompsonNonamenability.DyadicPLWitness.uniformOfRefines

uniformPartition def

The actual uniform mesh, with no extra partition hypothesis. · OAI.QuantitativeVanDerWaerden.uniformPartition

UniformProperInfiniteFactorStability def

The properly infinite factor case, with the tolerance uniform over all separable representations. · OAI.KadisonKastler.UniformProperInfiniteFactorStability

uniformRange def

The range of a small ground family all of whose entries have the same literal support. This is an actual HS name, not an external evaluated set. · OAI.PartitionConsistency.SetForcingNames.SymmetricSystem.uniformRange

uniformRangeInverse def

The sequence range admits an internal injection into its ground index set. This implements the least-occurrence argument with an actual HS graph; it does not assume that all its values are ground or that equalities of values can be decided … · OAI.PartitionConsistency.SetForcingNames.SymmetricSystem.uniformRangeInverse

uniformResidueCollision def

Probability that two uniform elements of s are congruent modulo p. · OAI.Ostmann.uniformResidueCollision

uniformResidueLaw def

A uniform residue modulo p, embedded into Fin B. The zero-weight padding allows different prime moduli to share the same sample type. · OAI.TwoPointCorrelations.uniformResidueLaw

UniformShape def

Uniform shape convergence gives the epsilon-radius estimate for all lattice endpoints inside a linearly growing ball. · OAI.GammaFPP.UniformShapeBridge.UniformShape

uniformSparsePrefactor def

An explicit absolute prefactor used before asymptotic absorption. · OAI.CoordinateSweeps.Grid.Holes.uniformSparsePrefactor

UniformSubexponentialETH def

The same single machine must meet every positive exponential rate, with one fixed polynomial input factor. Constants may depend on the chosen rate. · OAI.ParityWL.Complexity.UniformSubexponentialETH

uniformSubsetInverse def

The same least-index graph restricted to an arbitrary supported set. The set need not have a literal representative among the indexed entries. · OAI.PartitionConsistency.SetForcingNames.SymmetricSystem.uniformSubsetInverse

UniformSweepMixingTarget def

A single number of sweeps works uniformly over deterministic initial decks. · OAI.BinaryCoordinateSweeps.UniformSweepMixingTarget

uniformSystem def

Every nonempty finite family of strict nonzero similarities admits positive normalized weights. The uniform choice is bookkeeping, not a geometric hypothesis. · OAI.EntropyRateDimension.Extensions.uniformSystem

uniformTable def

Total fixed-arity dispatcher. Invalid arities use the six-site branch. · OAI.ContinuumCoulomb.QuantumPaddedTable.uniformTable

UniformTimeBounds def

Bounds uniform in the spatial point (or a spatial derivative index). · OAI.ForcedComputation.UniformTimeBounds

union def

Union of names for the chosen forcing order. · OAI.PartitionConsistency.SetForcingNames.ConditionAction.Name.union

union def

Combining two plateaux preserves their union and the L² Laplacian. · OAI.RegularPointCoordinates.RegularCompactCutoff.union

UnionEdges def

A small type indexing the three conditions used by the union-name construction: the two existing edge conditions and their common strengthening. · OAI.PartitionConsistency.SetForcingNames.UnionEdges

unionFamily def

All unions of k members of a family. · OAI.TalagrandDiscreteConvexity.unionFamily

unionLift def

A compatible family of arbitrary monoid homomorphisms glues over an actual directed union. · OAI.PartitionConsistency.ConservativeMonoids.Subobject.unionLift

unionName def

The union name for an arbitrary set forcing, not necessarily one with binary meets. Every common strengthening is included. · OAI.PartitionConsistency.SetForcingNames.unionName

unionTuple def

Exactly k entries, with no distinctness or disjointness restriction. · OAI.TalagrandDiscreteConvexity.unionTuple

unionTuple def

A union of exactly k entries; repetitions are allowed. · OAI.TalagrandDiscreteConvexity.unionTuple

UniqueEdges def

Every undirected edge has exactly one entry in the oriented enumeration. Thus refinement replaces genuine graph edges, not a multiset of edges. · OAI.ForestSpace.Diamond.Network.UniqueEdges

unit def

Every change of the named U,Q bases induces this invertible matrix on the free module of extension entries. Inverses are polynomial in the inverse base-change entries retained in the GL presentation. · OAI.IntegralCharacterVarieties.HomTransport.unit

unit def

The concrete unit into the realization of lambda. · OAI.Thomason.Construction.StrictOmegaCategory.Abelianization.unit

unit def

Kill all cells above n by their source, imposing the necessary n-cell relation. · OAI.Thomason.Construction.StrictOmegaCategory.IntelligentTruncation.unit

unitalCompletelyPositiveToContinuousLinearMap def

A unital completely positive map, bundled for the closed-range argument. · OAI.KadisonKastler.unitalCompletelyPositiveToContinuousLinearMap

UnitalCStar structure

A nonzero unital complex C*-algebra. · OAI.NuclearUltrapower.UnitalCStar

unitalizedExtension def

A unital representation retaining the zero extension of every original algebra element. The added unit acts on the full ambient Hilbert space. · OAI.KadisonSimilarity.unitalizedExtension

unitalOperatorRep def

The Hilbert-ultraproduct operator action is unital, including zero spaces. · OAI.NuclearUltrapower.HilbertUltraproduct.unitalOperatorRep

unitalStructureAlgebra def

The controlled structure algebra with its actual identity operator. · OAI.CoarseAssembly.DiscreteRoe.unitalStructureAlgebra

UnitarilyEquivalent def

Naimark's problem asks whether a $C^*$-algebra whose nonzero irreducible representations are all unitarily equivalent must be an algebra of compact operators. The formalization gives a counterexample in ZFC: a unital infinite-dimensional … · OAI.NaimarkZFC.UnitarilyEquivalent

Unitarizable def

Unitarizability at an explicitly quantified Hilbert-space universe. · OAI.Dixmier.Unitarizable

unitary def

The coordinate unitary is constructed from the finite matrix-unit columns. · OAI.KadisonSimilarity.FiniteOrthogonalColumns.unitary

unitary def

Coordinate unitaries act unitarily on the completed Hilbert ultraproduct. · OAI.NuclearUltrapower.HilbertUltraproduct.unitary

UnitaryBundleEquiv structure

A fiberwise unitary equivalence compatible with the actual total-space topologies, even when the bundle models use different coordinates. · OAI.Kaplansky.UnitaryBundleEquiv

unitaryCircleCFC def

Actual circle functional calculus in the supplied C*-algebra. · OAI.KadisonKastler.unitaryCircleCFC

unitaryCocycleDefect def

The supremum of all cocycle errors. · OAI.KadisonKastler.unitaryCocycleDefect

unitaryCocycleError def

The cocycle error as a bounded function of the two group variables. · OAI.KadisonKastler.unitaryCocycleError

unitaryConj def

Conjugation by an ambient unitary operator. · OAI.KadisonKastler.unitaryConj

unitaryConjugacyOrbit def

Unitary conjugates of an element, as an actual subset of the algebra. · OAI.KadisonKastler.unitaryConjugacyOrbit

unitaryConjugate def

The orbit of a bounded operator under a representation. · OAI.KadisonSimilarity.unitaryConjugate

unitaryConjugateAlgebra def

A concrete von Neumann algebra conjugated by an ambient unitary. · OAI.KadisonKastler.unitaryConjugateAlgebra

unitaryConjugateEquiv def

Exact star-algebra equivalence with the conjugated concrete algebra. · OAI.KadisonKastler.unitaryConjugateEquiv

unitaryConjugateHom def

The inner automorphism restricted to the original algebra. · OAI.KadisonKastler.unitaryConjugateHom

UnitaryConjugationInvariant def

Invariance under simultaneous conjugation of all matrix arguments. · OAI.KadisonSimilarity.UnitaryConjugationInvariant

unitaryConjugationLinear def

Inner conjugation, with its linear-map structure. · OAI.KadisonKastler.unitaryConjugationLinear

UnitaryDoubleErgodic def

The exact double-ergodicity property with unitary coefficients used below. It is the bounded-map specialization of Björklund's Theorem 2.1, Remark 2.2 (arXiv:1406.0763), for a symmetric Poisson boundary. · OAI.KadisonKastler.UnitaryDoubleErgodic

unitaryDoubleOrbit def

One actual sample of the two-sided unitary orbit. · OAI.KadisonKastler.unitaryDoubleOrbit

unitaryDualEquiv def

Unitary conjugation acts isometrically on bounded scalar functionals. · OAI.BoundedHochschild.KadisonRingrose.unitaryDualEquiv

unitaryEquiv def

Forgetting the metric wrapper preserves every genuine unitary of the original factor. · OAI.Generator.FactorTraceUnitary.unitaryEquiv

unitaryEval def

Pointwise evaluation of a unitary representative is an actual unitary. · OAI.KadisonKastler.WeakOperatorRepresentative.unitaryEval

unitaryFamilyEval def

Evaluation of an actual uniformly bounded unitary family. · OAI.KadisonKastler.unitaryFamilyEval

unitaryHaarPolynomial def

The scalar-recovery polynomial, normalized by the square root of N. · OAI.KadisonKastler.unitaryHaarPolynomial

unitaryHaarSum def

The first N positive powers of a unitary. · OAI.KadisonKastler.unitaryHaarSum

unitaryInAlgebra def

Regard an ambient unitary contained in an algebra as a unitary of it. · OAI.KadisonKastler.unitaryInAlgebra

unitaryOrbitHull def

The closed convex orbit used in the fixed-point construction of a trace. · OAI.BoundedHochschild.KadisonRingrose.unitaryOrbitHull

unitaryPredualAction def

Pullback by the inverse unitary gives a left group action on the predual. · OAI.BoundedHochschild.KadisonRingrose.unitaryPredualAction

unitaryPullback def

Pull a functional back along conjugation by a unitary. · OAI.BoundedHochschild.KadisonRingrose.unitaryPullback

unitaryQuarterPath def

Restrict a uniformly controlled angular path to its quarter-turn interval. · OAI.WeakPureInfiniteness.unitaryQuarterPath

unitaryReplacement def

A unitary-valued extension of polar retraction. Away from invertibles it is set equal to 1. · OAI.NuclearUltrapower.unitaryReplacement

unitaryRepresentation def

This declaration is an exact comparator-selected statement. Read the Lean statement below for its mathematical content. · OAI.CubeShuffle.Specht.unitaryRepresentation

unitarySequence def

Arbitrary coordinate unitaries are bounded, without a dimension bound. · OAI.NuclearUltrapower.VariableUltra.unitarySequence

unitarySpectrumAngle def

Angular coordinates on the spectrum, taken in the quotient circle. · OAI.KadisonKastler.unitarySpectrumAngle

unitarySpectrumCircle def

The unitary spectrum as a continuous map into the circle. · OAI.KadisonKastler.unitarySpectrumCircle

unitaryState def

A diagonal entry after unitary conjugation is a positive unital state. · OAI.SharpLiebThirring.MatrixProof.unitaryState

unitBall def

The operator-norm closed unit ball, as a subset of the ambient operators. · OAI.KadisonKastler.unitBall

unitBoxStep def

Invalid vectors get harmless stationary rows. Every actual profile row is exactly the computed sampler transition transported to the box. · OAI.ContingencyTables.SmallGraphProfiles.unitBoxStep

unitCell def

The finite table of the additive classes of a strict cell's faces. · OAI.Thomason.Construction.StrictOmegaCategory.Abelianization.unitCell

unitClass def

The actual class of a sequence of unit vectors. · OAI.Tingley.unitClass

unitCornerEquiv def

The unit corner is canonically the original algebra. · OAI.BoundedHochschild.KadisonRingrose.unitCornerEquiv

unitCornerTrace def

The original trace restricted along the canonical unit-corner equivalence. · OAI.BoundedHochschild.KadisonRingrose.unitCornerTrace

unitCurvatureCoordinates def

The curvature-one algebraic tensor in arbitrary coordinates. · OAI.PositiveEinsteinFour.Geometry.unitCurvatureCoordinates

unitCurve def

The literal interpolation on the unit interval. · OAI.HyperbolicObstruction.SegmentChain.unitCurve

unitCyclicMonoid def

The ordinary cyclic additive submonoid generated by the order unit. · OAI.Kaplansky.unitCyclicMonoid

unitDirection def

Euclidean normalization, expressed using the finite-coordinate dot product. · OAI.ClosedSurfaceR4.RadialMetricAlgebra.unitDirection

UnitDiskCrosscutSeparation def

Exactly two open connected components, with the stated relative frontier. The endpoints belong to the circle and the open arc belongs to the disk. · OAI.CircleDomainRigidity.UnitDiskCrosscutSeparation

unitEquiv def

An orthogonal, unit-normal coordinate system, before forgetting the product L² norm. · OAI.Problem358.TangentNormalCoordinates.unitEquiv

unitExtensionBasis def

Completely explicit stabilization of a boundary-basis presentation. · OAI.EilenbergGanea.unitExtensionBasis

unitFinite def

Primal unit coordinate and its canonical image in the completion. · OAI.DiamondDistortion.SegmentSystem.unitFinite

unitFrameTensor def

The constant-curvature tensor in an orthonormal frame. · OAI.PositiveEinsteinFour.Geometry.unitFrameTensor

unitHomPresheafIso def

Evaluation at one is an isomorphism of module presheaves, not just a bijection on global morphisms. · OAI.CoherentDual.unitHomPresheafIso

unitHomSheafIso def

The genuine internal Hom from the structure sheaf is the target sheaf. · OAI.CoherentDual.unitHomSheafIso

unitIdempotent def

The free module of rank one, represented by the one by one identity matrix. · OAI.TorsionFreeBass.unitIdempotent

unitizationRangeRepresentation def

The original algebra acts unitally on the range of its own unit, even though its inclusion into its unitization is nonunital. · OAI.KadisonSimilarity.unitizationRangeRepresentation

unitizationRestrict def

Restrict through the functorial map between the two unitizations. · OAI.KadisonSimilarity.unitizationRestrict

unitizationRestrictionFiberEquiv def

Restriction preserves the range Hilbert space up to its canonical identity-on-vectors isometry. · OAI.KadisonSimilarity.unitizationRestrictionFiberEquiv

unitLabelsEquiv def

The unit induces a bijection on Boolean object labels. · OAI.Thomason.Construction.FiniteReflectionInput.unitLabelsEquiv

unitLaw def

Lebesgue probability on the unit interval. · OAI.Problem358.IntervalMidpoint.unitLaw

unitLineEquiv def

A feasible line on two unit coordinates has one point for each second coordinate. · OAI.Ostmann.unitLineEquiv

UnitList def

Unit-fraction lists in the intermediate construction may repeat denominators. · OAI.Problem337.TerminalDescent.UnitList

UnitListAtMost def

Length-bounded positive unit-fraction lists; repetitions are allowed at this stage of the density construction. · OAI.Problem337.Descent.UnitListAtMost

unitLocalEquiv def

The expected free rank-one evaluation law, with the local ring action. · OAI.CoherentDual.unitLocalEquiv

unitMap def

Normal coordinate followed by tangential displacement. · OAI.Problem358.TangentNormalCoordinates.unitMap

unitNormal def

Unit transverse vector of a nonzero reference normal. · OAI.Problem358.AffinePlaneGraph.unitNormal

UnitNuclearData structure

Unit-charge inputs carry no independently chosen charge parameters. · OAI.ContinuumCoulomb.UnitNuclearData

unitObjectsEquiv def

The resulting canonical equivalence of object sets. · OAI.Thomason.Construction.FiniteReflectionInput.unitObjectsEquiv

unitOuterDraw def

Each trial reads a disjoint word; failed trials use the feasible fallback. · OAI.ContingencyTables.SmallGraphProfiles.unitOuterDraw

unitPacketJet def

The actual Frechet derivative of the ideal packet, retained as a continuous linear map rather than only its finitely many rays. · OAI.HarmonicCounterexample.FiniteControl.SmoothWord.unitPacketJet

unitPhase def

The unit-modulus exponential used in the first-derivative sum. · OAI.Problem337.ReciprocalPhase.unitPhase

unitPiece def

An unrestricted integrable root term is a legitimate size-one piece. · OAI.LocalCancellation.unitPiece

unitPiece def

An unrestricted integrable root term is a legitimate size-one piece. · OAI.SignedDisk.LocalCancellation.unitPiece

unitRep def

Choice selects actual unit representatives after surjectivity is proved. · OAI.Tingley.unitRep

unitRootPair def

The explicit standard etale pair for adjoining an n-th root of a unit. · OAI.KummerEtale.unitRootPair

UnitsAt def

The same word lists that specify ranges also specify product-unit tests. The interval endpoints are irrelevant for this additional support family. · OAI.Ostmann.WordRangeDecoration.UnitsAt

unitSequence def

Every sequence of unit vectors is uniformly bounded. · OAI.Tingley.unitSequence

UnitSliceProperty def

Every nonempty unit-ball slice contains an almost antipodal unit vector. · OAI.ExactModuli.UnitSliceProperty

UnitSliceWidth def

Canonical width formula; negative values signify an empty slice. · OAI.Nagata.W04.UnitSliceWidth

unitSphereFlux def

Actual complex Bochner integral against Euclidean unit-sphere area. · OAI.Mahler.unitSphereFlux

unitSum def

A character sum over the units of a finite ring, written as a sum over the whole ring so that product-ring factorization is transparent. · OAI.Problem337.RamanujanProduct.unitSum

unitTangentCotangentEquiv def

Actual radial unit tangent coordinates and nonzero cotangent coordinates in a fixed manifold chart are mutually inverse. · OAI.PositiveEinsteinFour.Geometry.unitTangentCotangentEquiv

unitTangentRadialFlow def

Radius is constant and multiplies the time of the unit-speed flow. · OAI.PositiveEinsteinFour.Geometry.unitTangentRadialFlow

unitTangentRadialSlabHomeomorph def

The restriction is the actual radial flow, with inverse negative time. · OAI.PositiveEinsteinFour.Geometry.unitTangentRadialSlabHomeomorph

unitTapeEquiv def

The single extra output tape occupies its unique local index. · OAI.MaxCutGames.Foundations.Complexity.PoweringGlobalEnumeration.unitTapeEquiv

unitTapeEquiv def

The single extra output tape occupies its unique local index. · OAI.UniqueGamesTheorem.Foundations.Complexity.PoweringGlobalEnumeration.unitTapeEquiv

unitTensor def

The scalar multiplication tensor, the multiplicative unit. · OAI.MatrixMultiplication.AuxiliarySeparation.unitTensor

unitTopBasis def

Multiplying the wedge of a cotangent basis by an ring unit still is a basis of the determinant line. · OAI.CanonicalCoordinates.unitTopBasis

UnitTreeBound def

A cut dyadic statement on one top. Used only at levels B polynomial in log d. · OAI.FourierLLogL.Period.UnitTreeBound

unitUniform def

Lebesgue probability on the closed unit interval. · OAI.GammaFPP.unitUniform

unitVectorProjection def

The ordinary rank-one orthogonal projector of a unit vector. · OAI.Kaplansky.unitVectorProjection

unitWord def

Embed all units into the physical modular-power register, when m<2^w. · OAI.ExactQuantumFactoring.OrderTrial.unitWord

universalAlignmentColumn def

Polynomial alignment columns; every lift is one linear combination of these columns. · OAI.MaxCutGames.Quadratic.universalAlignmentColumn

universalAlignmentColumn def

Polynomial alignment columns; every lift is one linear combination of these columns. · OAI.UniqueGamesTheorem.Quadratic.universalAlignmentColumn

UniversalCommutatorTheorem def

The existence of a single numerical constant in Theorem thm:universal. · OAI.KadisonSimilarity.UniversalCommutatorTheorem

UniversalGNS abbrev

The Hilbert sum of the cyclic representations of all positive functionals. · OAI.BoundedHochschild.KadisonRingrose.UniversalGNS

UniversalGNS abbrev

Universal GNS Hilbert space, with all positive functionals as coordinates. · OAI.NuclearUltrapower.UniversalGNS

universalGNS def

The faithful unital Hilbert representation obtained by summing the GNS representations of all positive functionals. · OAI.NuclearUltrapower.universalGNS

universalGNSRepresentation def

Every C*-algebra acts on the Hilbert sum of its positive cyclic representations. · OAI.BoundedHochschild.KadisonRingrose.universalGNSRepresentation

UniversalHyperreflexivity def

The quantitative conclusion of Corollary cor:hyperreflexivity, with the same constant as the universal commutator theorem. · OAI.KadisonSimilarity.UniversalHyperreflexivity

universalJetCoefficient def

An actual Taylor coefficient polynomial, without a binomial-formula assumption. · OAI.Nagata.W27.universalJetCoefficient

universalLinearForm def

The universal coordinate z_i(t) with the x_ij as indeterminates. · OAI.MaxCutGames.Quadratic.universalLinearForm

universalLinearForm def

The universal coordinate z_i(t) with the x_ij as indeterminates. · OAI.UniqueGamesTheorem.Quadratic.universalLinearForm

UniversalModularCoisometries def

A concrete all-vector coisometry property; the spatial product below supplies it by the already constructed remote matrix sequences. · OAI.KadisonKastler.UniversalModularCoisometries

universalNorm def

The universal C*-seminorm over all Cuntz models. · OAI.NuclearUltrapower.CuntzPolynomial.universalNorm

universalNorm def

The full, not the reduced, universal C*-seminorm. · OAI.NuclearUltrapower.GroupStarAlgebra.universalNorm

universalPairMinor def

A two-row determinant, with subtraction equal to addition in characteristic two. · OAI.MaxCutGames.Quadratic.universalPairMinor

universalPairMinor def

A two-row determinant, with subtraction equal to addition in characteristic two. · OAI.UniqueGamesTheorem.Quadratic.universalPairMinor

universalSeminorm def

The universal model supremum is a submultiplicative seminorm. · OAI.NuclearUltrapower.CuntzPolynomial.universalSeminorm

universalSeminorm def

The universal model supremum is a submultiplicative seminorm. · OAI.NuclearUltrapower.GroupStarAlgebra.universalSeminorm

UniversalStabilityPublishedInputs structure

Perturbation and decomposition hypotheses for universal strong stability, including type I injectivity, infinite-factor projection structure, central decomposition, and Dixmier averaging. · OAI.KadisonKastler.UniversalStabilityPublishedInputs

UniversalStrongStability def

Universal strong stability, at an arbitrary fixed universe level. · OAI.KadisonKastler.UniversalStrongStability

universalSubdivision def

The subdivided universal identity simplex, as a chain in that same simplex. · OAI.Kaplansky.universalSubdivision

UniversalSupport def

Every ordered distinct tuple supports a nonzero equation with the given multiplicity vector. This is a definition of the intermediate universal system, not an assumption about which such systems exist. · OAI.Nagata.W13.UniversalSupport

universalTranslate def

Translation with indeterminate point coordinates. The coefficients are actual polynomials in the point variables. · OAI.Nagata.W27.universalTranslate

universalUnit def

These are general linear transports, not only matrices with nonvanishing determinant at complex points. · OAI.IntegralCharacterVarieties.FiniteMatrixPresentation.universalUnit

universalWeakPreserving abbrev

Every cobase change of the attaching map preserves weak maps. · OAI.Thomason.Construction.CobaseChangeCellularClosure.universalWeakPreserving

universeLift def

Raise the universe without changing any product-state data. · OAI.KadisonKastler.PointedMatrixProduct.universeLift

unlabel def

Undo a column relabelling on actual finite switching paths. · OAI.PlanarL1.Columns.Model.Path.unlabel

unlabel def

The point map keeps the height and moves only the column name. · OAI.PlanarL1.Columns.Model.Point.unlabel

unmerge def

Unmerge after trimming. The outer boundaries may be absent and the outer cells may be arbitrarily dirty. Only the two displayed cut cells are tested. · OAI.FiniteAlgebraicEnvelopes.Compiler.Surface.unmerge

Unopposed def

A protected indexed side has no oppositely indexed side anywhere in the input. A single oriented exterior polygon satisfies this condition literally. · OAI.HyperbolicObstruction.PictureSwitch.WalkPicture.Unopposed

unorderedPair def

p = {x,y}. · OAI.PartitionConsistency.SetLanguage.unorderedPair

UnorientedPublishedInputs structure

The precise covering/topological inputs needed after the oriented classification. The Euler and Betti statements concern the actual cover manifold; the antipodal quotient is proved from its metric data. · OAI.PositiveEinsteinFour.UnorientedPublishedInputs

unpack def

Parse as a frame. Arbitrary result on malformed. · OAI.Fifths.Bin.unpack

unpackRecord def

Remove one self-delimiting record; produce its reversed binary word. · OAI.RationalHitting.StackLanguage.unpackRecord

unplug def

Unplug an edge from its face cycle; the edge becomes a singleton cycle. · OAI.KaplanskyCounterexample.Planar.unplug

unplugCycleEquiv def

Splicing a nontrivial cycle at a point adds exactly one singleton cycle. · OAI.KaplanskyCounterexample.Planar.unplugCycleEquiv

unprotected def

Classes containing none of a fixed set of signed protected labels. · OAI.TwoWayComplementation.Diagram.unprotected

unsafeSet def

The small-tip neighborhood on the actual oriented double. · OAI.TriangularBilliards.unsafeSet

unsignedShift def

Reindex P by b, retaining the original differential. This is what the resolution computes. · OAI.LittleFinitistic.OrdinarySimulation.unsignedShift

unskippedGroupFailure def

The actual per-group failure test uses the rational estimated costs. · OAI.EditApproximation.unskippedGroupFailure

unskippedGuardWithWork def

All numerical acceptance tests after a nonempty band has been built. · OAI.EditApproximation.BinaryFraction.unskippedGuardWithWork

unswappedRow def

Apply a row in visiting order; source U is this composition with its physical sites listed N,...,1, since the rightmost matrix acts first. · OAI.CriticalHoneycomb.Transfer.PlanarNormalization.unswappedRow

untouched def

Count the vertices missed by the selected edges. · OAI.AsymptoticallyMinimalLittlewood.Nibble.untouched

Untwisted def

A table with no coordinate twisting on any chart. · OAI.FiniteAlgebraicEnvelopes.TwistedBrinThompson.Untwisted

untwistedSum def

Detect the missing untwisted relators by an actual abelian quotient of the partially presented group. This is a diagnostic, not the desired endpoint. · OAI.FiniteAlgebraicEnvelopes.TwistedBrinThompson.Generators.untwistedSum

untwistSubrep def

The same invariant subspaces for ρ and its sign twist. · OAI.CoordinateSweeps.SparseDimension.untwistSubrep

unweightedAttractor def

Literal set of all coding limits for the unweighted similarity family. · OAI.EntropyRateDimension.Extensions.unweightedAttractor

up def

The opposite shift. · OAI.Problem346.PolynomialShift.up

uParentPath def

U route: split tilde-b, interchange a,b, merge a,h. · OAI.IntegralCharacterVarieties.OccurrenceIncidence.ComplementaryPatch.uParentPath

Update structure

Data determining an update. · OAI.FourierLLogL.Dyadic.Thermal.Update

update def

The rational single-spin field update. · OAI.BufferedIsing.DSS.update

update def

Literal fixed-capacity pending-node controller. The current modulus is removed and this very node's distinct p−1 children are prepended in sorted order. An empty queue is an idle tick, not a new root query. · OAI.ExactQuantumFactoring.PhysicalTree.update

update def

A fixed noncomputable selection, only from the currently supplied data. · OAI.KServer.AdaptiveMinimization.Family.update

update def

Replacing one residual stem, and adjoining the released radial tails to all other stems, preserves literal disjoint exterior routes. · OAI.PlanarL1.Topology.ExteriorPorts.update

update def

The exact coordinate update used at product syntax. · OAI.PureTypeSystem.ObservationValues.Base.update

updateCenters def

The heavy update deletes all centers at distance at most 100r, then inserts x. · OAI.UniformKServer.HeavyPilot.updateCenters

updateCoordinate def

A canonical depth update, with no caller-dependent decidable-equality instance. This is extensionally the ordinary function update. · OAI.DilutedSpinGlass.updateCoordinate

UpdatesOK structure

Regularity and scalar bounds for the covariance update. · OAI.GeneralMahler.UpdatesOK

upgrade def

View a derivation as linear over any coefficient algebra that it kills. · OAI.StableCoordinate.DerivationScalarUpgrade.upgrade

upholstery def

prepare data structure pack (stamped fields plus x entries). Also need original chips tape. · OAI.PowerSaving.RAM.upholstery

upper def

Least nonnegative upper arrays evaluated at the root. P and Q are kept separately; changing their root combination changes the norm. · OAI.DiamondDistortion.RecursiveModel.upper

upperBlock def

Upper diagonal block of the regularized Hessian. · OAI.Problem356.LocalHessian.upperBlock

upperCalibration def

The actual upper foliation's spatial gradient at a point above the cone. · OAI.Bernoulli.DeSilvaJerison.upperCalibration

upperClamp def

On the comparable subposet, raise vertices below v to v. · OAI.Thomason.Construction.PosetGeometry.upperClamp

upperCollapse def

The common upper endpoint g in the local zigzag. · OAI.Thomason.Construction.SieveRetraction.upperCollapse

upperConstant def

The classical upper Chebyshev constant, approximately 1.10555. · OAI.Problem337.ChebyshevUpperSharp.upperConstant

upperCylinderMass def

The observed mass integrates over the entire unit vertical period. · OAI.ForcedComputation.ExpandingDetector.upperCylinderMass

upperFace def

The face omitting the upper occurrence of the cut vertex. · OAI.Thomason.Construction.PrismBarycentric.upperFace

UpperHit def

Coordinate form of membership in the second intercept cylinder. · OAI.TriangularCovering.UpperHit

upperInverse def

Inverse of the upper divisor-sum transform, expressed through ordinary Möbius inversion after complementing divisors. · OAI.Problem337.SelbergOptimal.upperInverse

upperLevelClip def

The scalar truncation on the interval from k to k+m. · OAI.RegularPointCoordinates.upperLevelClip

upperLevelPart def

The upper positive part is a contraction fixing zero for nonnegative levels. · OAI.RegularPointCoordinates.upperLevelPart

upperParameter def

Leaf parameter above the minimizer candidate. Its defining equation is proved from the actual glued DSJ profiles; it is not a new foliation assumption. · OAI.Bernoulli.DeSilvaJerison.upperParameter

UpperQuotient def

The genuine upper-end quotient rule, expressed without choosing a quotient presentation of the edge object. · OAI.KLInvariance.MomentGraph.GradedSheaf.UpperQuotient

upperSigned def

The actual signed glued DSJ upper profile, including the symmetry axis. · OAI.Bernoulli.DeSilvaJerison.upperSigned

upperSimple def

The larger of x and s*x in Bruhat order. · OAI.KLInvariance.upperSimple

upperSpectralCut def

The open upper spectral cut (t,∞) of a selfadjoint operator. · OAI.KadisonSimilarity.upperSpectralCut

upperTerm def

The part of the boundary incident to the top vertex. · OAI.CubicalChains.upperTerm

upperValue def

Value of an upper product gate before relabelling the gate types. · OAI.Problem335.IndexedDepth5Circuit.upperValue

upTensor def

The three-leg tensor at one actual up triangle center. Its empty state has weight one, and each of the three simple passages has exactly one κ. · OAI.CriticalHoneycomb.Transfer.PhysicalTiles.upTensor

upward def

Upward change in the exact finite candidate infimum. · OAI.GammaFPP.FiniteLocal.upward

upwardShadow def

The upward shadow of a ball, with a slightly larger rectangular base. · OAI.SLEExactGauge.upwardShadow

upwardSubmodule def

The same kernel, typed in the graded stalk so base-field instances are explicit. · OAI.KLInvariance.MomentGraph.GradedSheaf.upwardSubmodule

uRadius def

The second radial contact uses the negative of the actual direction w. · OAI.Tingley.uRadius

used def

Only the at-most-three sampled words actually present are charged by the probability bound, even when some input indices coincide. · OAI.SmoothObstruction.ShiftComparisons.used

used def

The symmetric set of precisely the darts used by the actual paths. · OAI.TorsionFreeZeroDivisors.SupportedImage.used

usedKeys def

The actual key image of a literal signature. · OAI.QuantitativeVanDerWaerden.SparsePerturbation.usedKeys

Uses def

Component restriction is attached only to a genuine point-source chart; the ordered formula is defined on every component of its recorded band. · OAI.PlanarL1.Columns.Model.BData.Uses