Glossary: K

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

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K abbrev

The homotopy category Kᵇ(C); boundedness is part of each object. · OAI.LittleFinitistic.BoundedHomotopy.K

K abbrev

K^b(proj-R), as a full subcategory with actual bounded f.g. projective representatives. · OAI.LittleFinitistic.FiniteProjectiveHomotopy.K

K abbrev

Section 3's K = Kᵇ(proj-B), with homotopy classes of chain maps. · OAI.LittleFinitistic.ProjectiveComplexes.K

K abbrev

A small type of precisely the source's probe multiplicity. · OAI.PartitionConsistency.ConcreteSystem.K

K abbrev

The logarithmic bound for the number of geometric levels. · OAI.Problem337.RawDensityParameters.K

K def

The closed tetrahedron in physical Euclidean coordinates. · OAI.TriangularCovering.K

kanBaseChangeWeak def

Weak equivalence after every base change along an actual Kan fibration. This is a property to be proved for cells, not an extra main-theorem input. · OAI.Thomason.Construction.kanBaseChangeWeak

kanExtensionComparison def

The actual comparison to the restriction of a larger total space. · OAI.Thomason.Construction.kanExtensionComparison

KanQuillenPublishedInput structure

The portion of the published Kan--Quillen theorem required by transfer, with all three classes fixed to their actual definitions. · OAI.Thomason.Construction.KanQuillenPublishedInput

kanReplacementFactorization def

The actual horn factorization of the map to the terminal simplicial set. · OAI.Thomason.Construction.kanReplacementFactorization

kanSimplexRestriction def

The canonical restriction map on total spaces above a simplex map. · OAI.Thomason.Construction.kanSimplexRestriction

KaplanskyColumnApproximation def

The matrix-column consequence of Kaplansky density (Blackadar, I.9.1.3), together with the C-star first isomorphism theorem and quotient norm lifting. The lifting bound has fixed slack 2. · OAI.KadisonSimilarity.KaplanskyColumnApproximation

kaplanskyFunction def

The scalar transform used in bounded approximation. · OAI.KadisonSimilarity.kaplanskyFunction

kaplanskyOffDiagonal def

The selfadjoint off-diagonal operator associated to a contraction. · OAI.KadisonSimilarity.kaplanskyOffDiagonal

kaplanskyPreimage def

The bounded inverse branch, defined by functional calculus. · OAI.KadisonSimilarity.kaplanskyPreimage

kappa def

Linear growth is enough for the normalization coding sizes · OAI.FourierLLogL.Dyadic.Thermal.kappa

kappa def

The multiplier in equation (15), with its exact rational coefficients. · OAI.PositiveEinsteinFour.Potential.kappa

kappa def

The weight in the stationary profile norm D. · OAI.StationaryNS.kappa

kappa def

The universal archimedean error mean, before any configuration is chosen. · OAI.WeakPinned.Grid.kappa

kazhdanSet def

An explicit finite set in the honest integral elementary subgroup. · OAI.NuclearUltrapower.Elementary.kazhdanSet

keepComponent def

Retain the connected component of an edge. · OAI.KaplanskyCounterexample.Planar.Ribbon.keepComponent

keepHead def

A recursive subnetwork is used ONCE, with its prefix wire retained. · OAI.ExactQuantumFactoring.BitArithmetic.SortedWords.keepHead

keepInterval def

The literal restricted successful matching, retaining an inserted word. · OAI.FKCRT.Inventory.StackMatching.keepInterval

keptEdges def

Edges remaining after DELETION, not pinning, of F. · OAI.BufferedIsing.keptEdges

kernel def

The degree -1 kernel in ker:transverse-expectation; its value at zero is zero. · OAI.BoltzmannNonuniqueness.TransverseAverage.kernel

kernel def

One row of a dyadic transition table, viewed as an exact rational law. · OAI.ContingencyTables.IntegerPropagation.kernel

kernel def

Exact probabilities for the symmetric nearest-neighbour walk on the integers. · OAI.FKCRT.SimpleWalk.kernel

kernel def

Restricted Newton kernel; c is its (positive) normalization. · OAI.HenonLaneEmden.IntervalGeometry.kernel

kernel def

The nonnegative, degree-normalized squared geometric sum. · OAI.Problem337.GeometricKernel.kernel

kernel def

Endpoint correction on the slow initial data. Both decaying factors are kept explicitly, as required in (future-kernel-graph). · OAI.SmoothObstruction.FiniteGreen.Splitting.Terminal.kernel

kernel def

Uniform sampling among all allowed nonzero labels. · OAI.SmoothObstruction.SymplecticSampling.kernel

kernel def

Exact two-dimensional rescaling ε⁻² ρ(x/ε). · OAI.TriangularBilliards.SpatialSmoothing.kernel

kernelApply def

Apply a finite real kernel. Output indices need no finiteness assumption. · OAI.MaxCutGames.Repetition.kernelApply

kernelApply def

Apply a finite real kernel. Output indices need no finiteness assumption. · OAI.UniqueGamesTheorem.Repetition.kernelApply

kernelAverage def

An actual average over the testing set, in the first kernel variable. · OAI.RegularPointCoordinates.kernelAverage

kernelChartHomeomorph def

A homeomorphism over the parameter base between the actual local kernel incidence space and the product with one fixed kernel. · OAI.Kaplansky.SmoothKernel.kernelChartHomeomorph

kernelCoefficients def

Collision blocks are sums of the rank-one matrices with that label value. · OAI.Dixmier.kernelCoefficients

kernelConjugateIso def

Transport a kernel through isomorphisms of its source and target. · OAI.CoherentDual.kernelConjugateIso

kernelCoordinateChange def

The fiber coordinate transition really is projection onto the second fixed kernel after reconstruction in the varying kernel. · OAI.Kaplansky.SmoothKernel.kernelCoordinateChange

kernelCutMaximum def

The unnormalized finite real sign-cut maximum. · OAI.JointDickman.kernelCutMaximum

kernelCutNorm def

The manuscript's normalization divides the sign maximum by N. · OAI.JointDickman.kernelCutNorm

KernelDerivative def

The derivative interface supplied by the inverse-norm calculus. · OAI.Problem356.GeometryJets.KernelDerivative

kernelDifference def

Hidden coordinates relative to one base matrix in the same row fiber. · OAI.MaxCutGames.Decoder.AdviceFibers.kernelDifference

kernelDifference def

Hidden coordinates relative to one base matrix in the same row fiber. · OAI.UniqueGamesTheorem.Decoder.AdviceFibers.kernelDifference

kernelEncoding def

The measurable phase encoding, defined without a measurable enumeration. · OAI.EuclideanFiveColor.PhaseEncoding.kernelEncoding

kernelEquiv def

Explicit linear identification of the actual kernels throughout the split neighborhood. Both maps are restrictions of the constructed projections. · OAI.Kaplansky.SmoothKernel.kernelEquiv

kernelEquiv def

The bounded determinant kernel has exactly the degree-< e polynomials as its parameters, including at e = 0. · OAI.MatrixMultiplication.AuxiliarySeparation.DeterminantBounds.kernelEquiv

kernelEquiv def

The kernel is canonically isomorphic to one polynomial copy. · OAI.MatrixMultiplication.AuxiliarySeparation.DeterminantKernel.kernelEquiv

kernelEquiv def

Exactly one freely chosen bit per active position parametrizes the kernel. · OAI.MaxCutGames.Soundness.KernelCardinality.kernelEquiv

kernelEquiv def

Identifies the actual linear kernel with the previously counted concrete kernel. · OAI.MaxCutGames.Soundness.PartnerLinear.kernelEquiv

kernelEquiv def

Exactly one freely chosen bit per active position parametrizes the kernel. · OAI.UniqueGamesTheorem.Soundness.KernelCardinality.kernelEquiv

kernelEquiv def

Identifies the actual linear kernel with the previously counted concrete kernel. · OAI.UniqueGamesTheorem.Soundness.PartnerLinear.kernelEquiv

kernelForm def

The finite coefficient pairing of a scalar kernel. · OAI.BoundedHochschild.KadisonRingrose.kernelForm

kernelHeat def

The canonical positive-time continuous representative defined by the kernel. · OAI.RegularPointCoordinates.kernelHeat

kernelHeightCast def

Transport along equality of total depths only; no change to a kernel. · OAI.DilutedSpinGlass.kernelHeightCast

kernelIdeal def

The common character kernel is a Lie ideal, not just a linear subspace. · OAI.PolycyclicRecognition.TriangularAdjoint.kernelIdeal

kernelIndicator def

The actual zero-image event for a linear map. · OAI.MaxCutGames.Gadget.ActualGadget.kernelIndicator

kernelIndicator def

The actual zero-image event for a linear map. · OAI.UniqueGamesTheorem.Gadget.ActualGadget.kernelIndicator

kernelMap def

Its kernel is the alpha-multiple of the twisted upper stalk. · OAI.KLInvariance.ReflectionPairTranslation.kernelMap

kernelMass def

The kernel mass controlling every jet, with absolute values for signed kernels. · OAI.ForcedComputation.BoundedSpatialJets.kernelMass

kernelMeasure def

The intrinsic ideal Haar measure transported to the exact kernel. · OAI.PolycyclicRecognition.CartanWordModel.MeasuredCone.kernelMeasure

KernelMinimal def

Minimality of the full outgoing boundary cover. The assignment formulation avoids dependent casts and is equivalent to the usual kernel containment. · OAI.KLInvariance.MomentGraph.GradedSheaf.KernelMinimal

kernelMonomial def

The kernel monomial (uw-vs) u^(e-1-j) v^j, with j < e. · OAI.MatrixMultiplication.AuxiliarySeparation.DeterminantKernel.kernelMonomial

kernelOfGame def

A projection game's predicate and actual question distribution determine the conditional kernel used by the collision argument. · OAI.MaxCutGames.Repetition.kernelOfGame

kernelOfGame def

A projection game's predicate and actual question distribution determine the conditional kernel used by the collision argument. · OAI.UniqueGamesTheorem.Repetition.kernelOfGame

kernelPreMap def

A map of labels bounded for the kernel quadratic form induces a bounded linear map on the finite kernel vectors. · OAI.BoundedHochschild.KadisonRingrose.kernelPreMap

kernelProjection def

The kernel projection is an actual measurable representative. · OAI.KadisonKastler.WeakOperatorRepresentative.kernelProjection

kernelPushforward def

Applying a finite stochastic kernel, forgetting its input. · OAI.MaxCutGames.Foundations.Repetition.kernelPushforward

kernelPushforward def

Applying a finite stochastic kernel, forgetting its input. · OAI.UniqueGamesTheorem.Foundations.Repetition.kernelPushforward

kernelQuotientHomeomorph def

The quotient homeomorphism respects the actual weak topologies. · OAI.EilenbergGanea.CubeRealization.kernelQuotientHomeomorph

kernelRealization def

The intrinsic ideal group and the actual kernel have the same topology and multiplication. · OAI.PolycyclicRecognition.kernelRealization

kernelRelativeEntropy def

A measurable version of conditional relative entropy, for dominated kernels. · OAI.InvariantIsing.kernelRelativeEntropy

kernelRows def

A nonzero row of a division-ring kernel expands into d independent ordinary kernel rows after a faithful d-dimensional representation. · OAI.RationalHitting.BlockDivision.kernelRows

kernels def

Index zero is the heat term; the other two indices are Cartesian derivatives. · OAI.ForcedComputation.PlaneScalarMild.kernels

kernelSourceOperator def

All three raw kernels define bounded source operators on the finite interval. · OAI.ForcedComputation.PlaneScalarMild.kernelSourceOperator

KernelTower def

Finite kernels depending on the full preceding path, before tilting. · OAI.DilutedSpinGlass.KernelTower

kernelTransport def

Application of a finite transition kernel. · OAI.TwoPointCorrelations.kernelTransport

kernelVector def

A bounded kernel vector, obtained by multiplication by uw-vs. · OAI.MatrixMultiplication.AuxiliarySeparation.DeterminantBasis.kernelVector

kernelVector def

The actual kernel vectors used at degree e: there are e of them. · OAI.MatrixMultiplication.AuxiliarySeparation.DeterminantKernel.kernelVector

Key abbrev

A complete proposed successor, including its source and target state. · OAI.OneWayLiveness.CellNetwork.Key

keyAnswer def

The actual verifier labeling, viewed as a function of exact affine keys. · OAI.MaxCutGames.Decoder.TableKeysRestoration.keyAnswer

keyAnswer def

The actual verifier labeling, viewed as a function of exact affine keys. · OAI.UniqueGamesTheorem.Decoder.TableKeysRestoration.keyAnswer

keys def

Exactly the keys attained by the finite source. · OAI.TalagrandDiscreteConvexity.FiniteFibers.keys

kids def

Children from the distinct prime fields, ignoring zero padding and 2. Repeated labels in DIFFERENT node records are not identified. · OAI.ExactQuantumFactoring.BitArithmetic.ChildQueue.kids

killed def

The walk killed on first visiting -1, with both endpoints nonnegative. · OAI.FKCRT.SimpleWalk.killed

killedHeat def

The killed heat kernel obtained from the proved discrete reflection principle. · OAI.FKCRT.SimpleWalk.killedHeat

KillsSpheres def

A ghost map in one geometric degree, including unbased spheres. · OAI.GroupRingTopology.Cellular.KillsSpheres

Kind inductive

Echo labels have k as the predecessor iteration number. · OAI.ExactDerandomization.Net.Kind

Kind inductive

Exactly the allowed vertex list, including reversal of splitting. The nonnegative numbers include every zero block before normalization. · OAI.IntegralCharacterVarieties.OccurrenceIncidence.VertexTable.Kind

Kind inductive

Pairing patterns at a layer, with the inequality omitted in the diagonal case. · OAI.Problem335.Pairings.Kind

KineticLocalFlow structure

A constructed local solution and its first variation. This is output of the local ODE theorem, not a geometric input. · OAI.PositiveEinsteinFour.Geometry.KineticLocalFlow

KineticTest structure

A smooth test, periodic in the spatial variable and compact in time and velocity. · OAI.BoltzmannNonuniqueness.KineticTest

kineticZeroDifferential def

The differential sends a momentum perturbation to its raised velocity; the position perturbation has zero rate at zero momentum. · OAI.PositiveEinsteinFour.Geometry.kineticZeroDifferential

KirchbergDerivationCriterion def

Kirchberg's derivation criterion (1996), as stated in Ozawa, An invitation to the similarity problems, Theorem 1.1, with boundedness supplied by Ringrose (1972), Theorem 2, p. 434. · OAI.KadisonSimilarity.KirchbergDerivationCriterion

KirchbergOInfinityAbsorption def

Nuclear strong pure infiniteness implies absorption for a separable algebra, including the zero algebra, without a unit or simplicity hypothesis. · OAI.WeakPureInfiniteness.KirchbergOInfinityAbsorption

kirchbergPath def

The imaginary direction of this path is unitary conjugation. · OAI.KadisonSimilarity.kirchbergPath

Kit structure

Sufficient resources and access for a family of offset trials. · OAI.Fifths.Single.Kit

Kit structure

all chip fields within budget · OAI.PowerSaving.RAM.Bench.Kit

kkDistance def

Kadison and Kastler's ordinary distance, without matrix amplification. · OAI.KadisonKastler.kkDistance

klFamilies def

The polynomial families selected by their equal-parameter normalization. · OAI.KLInvariance.klFamilies

KLSStatement def

The full dimension-free statement: one constant works for every dimension, every isotropic log-concave density, and every smooth compactly supported test. · OAI.LeanBlast.KLS.KLSStatement

kmsNeighborsEquiv def

Extrinsic submodule neighbors and the finite KMS neighbor predicate agree. · OAI.MaxCutGames.Inverse.MatrixChart.kmsNeighborsEquiv

kmsNeighborsEquiv def

Extrinsic submodule neighbors and the finite KMS neighbor predicate agree. · OAI.UniqueGamesTheorem.Inverse.MatrixChart.kmsNeighborsEquiv

knotPermutation def

Move the inserted t² label to the last index, leaving M in its original order. This is only a simultaneous change of basis of the actual pencil. · OAI.CriticalHoneycomb.FiniteFunctional.StripAsymptotic.knotPermutation

KoebeCircleDomainConjecture def

Paper 047-02, Introduction, thm:main: unrestricted Koebe uniformization. · OAI.CircleDomainRigidity.KoebeCircleDomainConjecture

koopman def

The actual Koopman operator, restricted to the full centered subspace. · OAI.ThreeTorus.koopman

koszulExponent def

The sign from reordering the odd factors, with positions ordered as in ordinary tensor words. There is no choice of orientation hidden here. · OAI.CoordinateSweeps.SignedTensor.koszulExponent

kProjectiveCoproductIsColimit def

An actual coproduct of K-projective cochain complexes with K-projective coproduct object remains a coproduct in the genuine derived category. · OAI.DerivedBar.kProjectiveCoproductIsColimit

kraus def

A finite Kraus sum, with the adjoint on the left. · OAI.MUB6.Weiner.kraus

kronecker def

Kronecker multiplicity is the complex dimension of Hom, with the diagonal symmetric-group action on the tensor product. · OAI.Saxl.kronecker

KummerPrimeSiegelWalfisz def

The raw prime-sum specialization. Cubes and the zero numerator are excluded explicitly; no smooth or structured-sum estimate is assumed. · OAI.CubicFirstMoment.KummerPrimeSiegelWalfisz

KWOmega abbrev

The countable product of unit intervals. · OAI.ExactModuli.KWOmega