Glossary: N

Definitions in this project whose names start with N. 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

n def

`Input.n` returns the stored number of vertices whether the graph was represented explicitly or by binary multiplicities. · OAI.AlgorithmicThinTrees.Input.n

n def

The second new linear coordinate, denoted N in the manuscript. · OAI.StableCoordinate.Linearization.n

N6 def

Maximum expressed as a supremum of attainable finite family sizes. · OAI.MUB6.N6

Name structure

Literal names for this condition set. Equality is equality of the underlying ZF sets, not equality of tree presentations. · OAI.PartitionConsistency.SetForcingNames.ConditionAction.Name

Name def

All hereditarily symmetric names, without any fixed bound on ranks. · OAI.PartitionConsistency.SetForcingNames.SymmetricSystem.Name

name def

The actual forward partition name, not an independent copy. · OAI.SmoothObstruction.PartitionEntropy.name

nameAtom def

The atoms of the joined partition through time N-1. · OAI.DukePrimeDegree.nameAtom

namedAccepts def

The incidence predicate as a game on the actual questions (o,n), with the retained slot left internal to the verifier. · OAI.MaxCutGames.Soundness.IncidenceExtraction.Incidence.namedAccepts

namedAccepts def

The incidence predicate as a game on the actual questions (o,n), with the retained slot left internal to the verifier. · OAI.UniqueGamesTheorem.Soundness.IncidenceExtraction.Incidence.namedAccepts

namedAtomicBand def

This is the very same obtained weighted atomic gallery, not a replacement chosen from its endpoints or ranks. · OAI.IntegralCharacterVarieties.OccurrenceIncidence.PortAssembly.namedAtomicBand

namedClip def

The old field has priority zero; the shield has priority one, and actual inherited atom identities are shifted by two. Thus a retaining tie keeps the old identifier, just as required by the source chart update. · OAI.PlanarL1.Interpolation.namedClip

namedGrade def

This is the graded module identified by the old seam, not merely an isomorphic module of the same rank. The formula on representatives is literal. · OAI.IntegralCharacterVarieties.OldContactSlice.namedGrade

namedQ def

The NAMED old quotient, modulo its extracted submodule, is the induced quotient-subsystem grade. · OAI.IntegralCharacterVarieties.OldContactSlice.namedQ

namedU def

A canonical extraction of the U-quotient into the named old grade. · OAI.IntegralCharacterVarieties.OldContactSlice.namedU

NamedValue structure

An atom evaluation together with its deterministic priority/inheritance name. Its value may depend on all the already sampled ancestor noises. · OAI.PlanarL1.Interpolation.NamedValue

nameEquiv def

Executable row-major encoding of the finite clone names. · OAI.MaxCutGames.Reduction.FiniteSource.nameEquiv

nameEquiv def

Executable row-major encoding of the finite clone names. · OAI.UniqueGamesTheorem.Reduction.FiniteSource.nameEquiv

nameInstruction def

Copy both symbols of a payload pair, or copy the name terminator. · OAI.MaxCutGames.BinaryTokenMachine.nameInstruction

nameInstruction def

Copy both symbols of a payload pair, or copy the name terminator. · OAI.UniqueGamesTheorem.BinaryTokenMachine.nameInstruction

names def

The canonical renaming is independent of every target vertex name. · OAI.TorsionFreeZeroDivisors.PatternCoding.names

nameSetoid def

The setoid of internal name codes; no recursion on membership is used. · OAI.PartitionConsistency.ForcingQuotient.AtomicData.nameSetoid

narrowed abbrev

mask a deterministic array to possibly narrower terminal slices. · OAI.ExactDerandomization.Est.Axis.narrowed

narrowRiseEvent def

The measurable supported event used to obtain the narrow first crossing. · OAI.SLEExactGauge.FirstHeightSupport.narrowRiseEvent

natBasis def

Exact bit representation used for modular-power values. · OAI.ExactQuantumFactoring.OrderTrial.natBasis

natBits def

Unary self-delimiting natural numbers. Outputs are explicit, not succinct. · OAI.DirectedFeedback.natBits

natCloneEquation def

Numeric machine target: no remainder, bounded-name proofs, or function lookup is needed in the three generated variable names. · OAI.MaxCutGames.Reduction.CloneTable.natCloneEquation

natCloneEquation def

Numeric machine target: no remainder, bounded-name proofs, or function lookup is needed in the three generated variable names. · OAI.UniqueGamesTheorem.Reduction.CloneTable.natCloneEquation

natCode def

Unary natural numbers have an explicit end marker, so prefix parsing never relies on an uncharged register-length operation. · OAI.Superstring.BitCode.natCode

natCode def

Self-delimiting binary code: ℓ ones, a zero, then ℓ low-to-high bits. This fixes one standard binary encoding rather than allowing a nonuniform advice string to be included in the input. · OAI.UniformKServer.natCode

natColor def

The ordered list is extended by its parent off its finite domain. Using a natural numbered occurrence makes all reindexing by equality transparent. · OAI.IntegralCharacterVarieties.OccurrenceIncidence.PortWiring.natColor

NatExprPoly def

Uniform polynomial growth of a family of literal natural expressions. Nothing here bounds the values of dynamic variables or assumes arithmetic is free. · OAI.ExactQuantumFactoring.NatExprPoly

native abbrev

The native finite-interval presentation of tensor by the actual Q_X. Its comparison to the ordinary total presentation is proved separately. · OAI.LittleFinitistic.SelectedBarComparison.native

nativeBarIso def

Natural identification of the native D(B-Mod) tensor by the actual bounded right-projective bimodule resolution and DerivedBar's genuine localized tensor, after chainToIntegerDerived. Both outside module actions are retained. · OAI.LittleFinitistic.BimoduleTotal.nativeBarIso

nativeBarIterateIso def

The augmentation comparison iterates naturally on the genuine localized chain category. This identifies actual derived functors, not only vector spaces. · OAI.LittleFinitistic.BimoduleTotal.nativeBarIterateIso

nativeBarResolutionIso def

The native derived tensor of the integer extension is computed on its genuine projective bar resolution, with no hypothesis on the input's terms. · OAI.LittleFinitistic.BimoduleTotal.nativeBarResolutionIso

nativeChainBarResolutionIso def

The same comparison written using the native chain-localization inclusion. · OAI.LittleFinitistic.BimoduleTotal.nativeChainBarResolutionIso

nativeCompatibility01 def

Actual arrow-01 compatibility with the native P, vertex functors and inclusions. · OAI.ExternalTensor.Section4.ArrowVertex.NativeBridge.nativeCompatibility01

nativeCompatibility12 def

Actual arrow-12 compatibility with the native P, vertex functors and inclusions. · OAI.ExternalTensor.Section4.ArrowVertex.NativeBridge.nativeCompatibility12

nativeEvaluation def

The exact native module-valued degree-zero evaluation, using the module's original compatible k action. · OAI.LittleFinitistic.BimoduleTotal.BoundedProjective.nativeEvaluation

nativeIso def

Both tensor presentations use the identical Q_X and signed finite total. · OAI.LittleFinitistic.SelectedOrdinaryOrbit.nativeIso

nativeIterate def

Iteration of the native full-left-action integer derived endofunctor. · OAI.LittleFinitistic.BimoduleTotal.nativeIterate

nativeIterateIndexedIso def

On degree-zero modules, the same native derived iteration is represented by the actual Section 6 indexed multibar with all module actions retained. · OAI.LittleFinitistic.BimoduleTotal.nativeIterateIndexedIso

nativeIterateMultibarIso def

The native iterate on an extended chain input is the manuscript's actual recursive bar total, with the endpoint-minus-tail and signed vertical differentials. · OAI.LittleFinitistic.BimoduleTotal.nativeIterateMultibarIso

nativeProjectiveModel def

Direct adapter for the boundedness and right-projectivity fields of the native fixed rectification. · OAI.LittleFinitistic.BimoduleTotal.nativeProjectiveModel

nativeSingleEvaluation def

Native degree-zero module embedding, with the module's original compatible scalar action. · OAI.LittleFinitistic.BimoduleTotal.BoundedProjective.nativeSingleEvaluation

nativeStalkIndexedIso def

Genuine native iteration on the native integer stalk, identified with the actual Section 6 indexed multibar. No bar comparison is supplied as a premise. · OAI.LittleFinitistic.BimoduleTotal.nativeStalkIndexedIso

nativeStochasticSuccess def

The native experiment samples a mask, then the actual coefficient tuple. The kernels may depend on these public choices but not on an opposite input. · OAI.MaxCutGames.Clean.StochasticBound.nativeStochasticSuccess

nativeStochasticSuccess def

The native experiment samples a mask, then the actual coefficient tuple. The kernels may depend on these public choices but not on an opposite input. · OAI.UniqueGamesTheorem.Clean.StochasticBound.nativeStochasticSuccess

natPolynomial def

A naturally indexed exponential sum, in the ordinary real phase variable. · OAI.Problem337.ThreePrimeContinuousEnergy.natPolynomial

natRowCount def

Number of matches assigned to a natural row index. · OAI.TreeEdit.BinaryLower.TaggedNonsplit.natRowCount

naturalCharacter def

A character evaluated on the natural numbers, with its usual zeros. · OAI.TwoPointCorrelations.naturalCharacter

naturalInputProgram def

Parse the actual marker bits of a binary natural number. · OAI.ContinuumCoulomb.ChargePrograms.naturalInputProgram

naturalIso def

Naturality holds on every chain map, including the added zero degrees. · OAI.LittleFinitistic.IntegerExtensionFunctor.naturalIso

naturalIso def

The native tensor of the actual Q_X agrees naturally with bar-derived tensor by the ORIGINAL X, with no remaining augmentation or action premise. · OAI.LittleFinitistic.SelectedBarComparison.naturalIso

naturalProduct def

Each list is evaluated as its actual natural product, with multiplicities. · OAI.Ostmann.MovingSlotReversal.naturalProduct

natWord def

Unary natural words with delimiters make the circuit description explicit. Unary wire addresses cause at most polynomial overhead when width is polynomial. · OAI.ExactQuantumFactoring.natWord

nbr def

Number of solutions as a real. · OAI.HadwigerCounterexample.nbr

nd def

finite mesh: t_j=j/200 · OAI.GeneralMahler.SCal.Grid.nd

near def

Membership in a closed graph ball of finite natural radius. · OAI.MetricEntropyDuality.PartitionGraph.near

nearBall def

Only the near-site region in pilot-local(2) uses a strict inequality. · OAI.KServer.Pilot.nearBall

NearBoundary def

Small-ball height loss is proximity to a genuine band boundary. · OAI.PlanarL1.Tiling.NearBoundary

nearbyLabels def

The finite list of intermediate-level choices near a base point. · OAI.DoublingHilbert.nearbyLabels

nearbyStripIndices def

A uniform finite set of strips meeting an interval shorter than 128 strip widths. · OAI.DoublingHilbert.nearbyStripIndices

NearColumns def

Geometric control of visits to a set of columns. The witnesses are actual points at heights in J and actual ambient-band distances from the center. · OAI.PlanarL1.Columns.Model.Point.NearColumns

NearConjugacy def

The conclusion of strong stability, with a strict displacement bound. · OAI.KadisonKastler.NearConjugacy

nearCut def

Uniformly bounded exceptional grid indices near one real cut. · OAI.TorsionFreeZeroDivisors.BlockAlignment.nearCut

nearCylinder def

The spatially truncated cylinder of cubical flags used in continuation. · OAI.SharpLiebThirring.CubeFlags.nearCylinder

nearest def

Classical choice is used only for the soundness analysis, not the output algorithm. · OAI.MaxCutGames.Foundations.PCP.CodeComposition.nearest

nearest def

The genuine nearest point; no fixed-point principle is used here. · OAI.PettyProjection.FixedPoint.nearest

nearest def

Classical choice is used only for the soundness analysis, not the output algorithm. · OAI.UniqueGamesTheorem.Foundations.PCP.CodeComposition.nearest

nearestDistance def

Minimum distance to the finite nonempty family of centers. · OAI.Paper320.nearestDistance

nearestInteger def

Rounding convention: half-integers are rounded upwards. · OAI.RuledApproximation.nearestInteger

nearestIntegerDistance def

Distance to the nearest integer, with rounding used only to select a minimizer. · OAI.Problem335.nearestIntegerDistance

NearInclusion def

The strict near-inclusion convention of the published input. Approximants belong to the algebra, but need not lie in its unit ball. · OAI.KadisonKastler.NearInclusion

nebulous def

Tiny cover exists after preparing retained mass, seen on its support. Requires each old tile contain only original support. · OAI.HadwigerCounterexample.PreparationParameters.nebulous

negativeAverage def

The finite negative-time average. · OAI.TriangularBilliards.Analysis.HilbertFlow.negativeAverage

NegativeBranchChildrenMatch def

The child identifications along each negative transverse branch. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NegativeBranchChildrenMatch

NegativeBranchFlagsHold def

The framed flag equations on each negative transverse branch. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NegativeBranchFlagsHold

NegativeBranchFrameMatch def

Compatibility of the transported frames across a negative transverse branch. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NegativeBranchFrameMatch

NegativeBranchFrameValuesAgree def

Equality of the two frame values on a negative transverse branch. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NegativeBranchFrameValuesAgree

NegativeBranchMirrorAttached def

The attachment of the reflected port of a negative transverse branch. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NegativeBranchMirrorAttached

NegativeBranchOriginalAttached def

The attachment of the original port of a negative transverse branch. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NegativeBranchOriginalAttached

NegativeBranchSameSeam def

The two ports of each negative transverse branch attach to the same seam. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NegativeBranchSameSeam

NegativeBranchSideValuesTrivial def

The side values on each negative transverse branch are trivial. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NegativeBranchSideValuesTrivial

negativeLeafMatch def

Match the common tail and each of finitely many range leaves. · OAI.WeakPureInfiniteness.negativeLeafMatch

negativeLeftLeaf def

The first half of the matched range leaves. · OAI.WeakPureInfiniteness.negativeLeftLeaf

NegativeLevel abbrev

The integral level downstairs; the action is by left multiplication by the height kernel. · OAI.EilenbergGanea.LevelTransport.NegativeLevel

negativeMoment def

An unlimited finite-family-size supremum, in ℝ≥0∞, includes the entire sum. · OAI.SharpLiebThirring.negativeMoment

negativeOrientationMatrix def

Coefficients of the negative two-form action. · OAI.PositiveEinsteinFour.QuaternionFrame.negativeOrientationMatrix

negativePhaseCoefficientSequence def

The actual negative coefficient bounded sequence. · OAI.KadisonKastler.negativePhaseCoefficientSequence

negativePhaseWordUnitary def

Negative word, already a full adjoint power. · OAI.KadisonKastler.negativePhaseWordUnitary

negativeResidue def

Natural-number label for the negative residue of a summand element. · OAI.Ostmann.negativeResidue

negativeRightLeaf def

The second half of the matched range leaves. · OAI.WeakPureInfiniteness.negativeRightLeaf

negativeRotationMatrix def

Smooth negative gradient written in the spanning infinitesimal rotations. · OAI.ArnoldCounterexample.CriticalBound.negativeRotationMatrix

negativeShift def

The first component of multiplication by uw-vs. · OAI.MatrixMultiplication.AuxiliarySeparation.DeterminantBounds.negativeShift

negTailResidues def

Residues of the negative of the other summand, with the same deletion. · OAI.Ostmann.negTailResidues

neighbor def

The other maximal flag sharing the facet obtained by deleting vertex j. · OAI.SharpLiebThirring.CubeFlags.Flag.neighbor

NeighborColor def

Colors retain their full history, and hence are shared between graphs. · OAI.WLIdentification.NeighborColor

neighborhood def

Availability is the manuscript's entire closed radius-one neighborhood of this full-column cell, not just tests at the finite original vertices. · OAI.PlanarL1.Columns.Model.MainFamily.neighborhood

neighborhoodEndpoints def

The anchor's closed circle neighborhood, realized by one real interval. An integer translate leaves every label and every width unchanged. · OAI.QuantitativeVanDerWaerden.AdaptiveMesh.neighborhoodEndpoints

neighbors def

The dependency graph obtained by sharing one of the assigned variables. · OAI.KaplanskyCounterexample.FiniteLocalLemma.neighbors

NeighborSamplingRow structure

Actual samples, root step and weak law, with no affine-limit premise. · OAI.PolycyclicRecognition.CartanWordModel.NeighborSamplingRow

neighborsEquivExtensionData def

Each neighbor has a unique intersection hyperplane and extension. · OAI.MaxCutGames.Inverse.MatrixChart.neighborsEquivExtensionData

neighborsEquivExtensionData def

Each neighbor has a unique intersection hyperplane and extension. · OAI.UniqueGamesTheorem.Inverse.MatrixChart.neighborsEquivExtensionData

neighborStates def

The state filter is applied after the quadratic coordinate scan. · OAI.ContingencyTables.CompanionArithmeticProposal.neighborStates

nerveCylinder def

The interval comparison on the Street nerve, evaluated on a simplex F : O_m → X and an ordinal map [m] → [1]. · OAI.Thomason.Construction.RightGrayInput.nerveCylinder

nerveHomotopy def

Every strict right Gray cylinder gives an actual simplicial homotopy. · OAI.Thomason.Construction.RightGrayInput.nerveHomotopy

nerveIso def

The subdivision has this face-poset as its nerve. · OAI.Thomason.Construction.NerveFaceChains.nerveIso

nerveLocalizer def

Any nerve with its inverse-image weak equivalences is a morphism of localizers. · OAI.Thomason.Construction.nerveLocalizer

nerveMapOfLabelsCarrierHomotopy def

A prescribed monotone carrier upper bound gives the comparison homotopy without requiring the labels themselves to be monotone. · OAI.Thomason.Construction.ChainLabelApproximation.nerveMapOfLabelsCarrierHomotopy

nerveMapOfLabelsHomotopy def

Labels with a common prescribed upper map give a homotopy to that map composed with the greatest-face comparison. · OAI.Thomason.Construction.ChainLabelApproximation.nerveMapOfLabelsHomotopy

nerveMapOfLabelsToSubcomplex def

The label map with its actual prescribed subcomplex as codomain. · OAI.Thomason.Construction.ChainLabelApproximation.nerveMapOfLabelsToSubcomplex

nerveNaturalHomotopy def

A natural transformation gives an actual simplicial interval homotopy. · OAI.Thomason.Construction.nerveNaturalHomotopy

nervePushoutComparison def

The canonical comparison retains the two original structure maps. · OAI.Thomason.Construction.nervePushoutComparison

Nested structure

A genuinely nested sequence of subsequences, with the usual diagonal map. · OAI.SeparableQuotient.PathSelection.Nested

nested def

Flatten a subrepresentation of a subrepresentation without changing its dimension. · OAI.CoordinateSweeps.SparseDimension.nested

nestedCornerEquiv def

A corner within a corner is the corner of its ambient projection. · OAI.BoundedHochschild.KadisonRingrose.nestedCornerEquiv

NestedCycle inductive

A finite nesting schedule. Only leaves supply actual emitter traces. Internal nodes supply concrete instruction placements and compatible endpoint schedules; their complete execution is derived below. Level q operates coordinate q, so … · OAI.MaxCutGames.Foundations.Complexity.MachineTupleOdometer.NestedCycle

NestedCycle inductive

A finite nesting schedule. Only leaves supply actual emitter traces. Internal nodes supply concrete instruction placements and compatible endpoint schedules; their complete execution is derived below. Level q operates coordinate q, so … · OAI.UniqueGamesTheorem.Foundations.Complexity.MachineTupleOdometer.NestedCycle

nestedEmbedding def

Compose the two actual quotient-domain and target-subspace embeddings. · OAI.MaxCutGames.Appendix.RestrictionTransport.nestedEmbedding

nestedEmbedding def

Compose the two actual quotient-domain and target-subspace embeddings. · OAI.UniqueGamesTheorem.Appendix.RestrictionTransport.nestedEmbedding

NestedFamily structure

Acceptance at a stronger index implies acceptance at every weaker index. · OAI.Paper320.NestedFamily

nestedMatrixEquiv def

Flattening two finite matrix indices is a star-algebra equivalence. · OAI.BoundedHochschild.KadisonRingrose.nestedMatrixEquiv

nestedPointIdeal def

The actual maximal point ideal in the nested bivariate polynomial ring. · OAI.Nagata.W18.nestedPointIdeal

nestedProductProfile def

The accumulated factor viewed as a function on its current partition. · OAI.LipschitzHilbert.nestedProductProfile

nestedToBivariate def

The inverse substitution sends inner X to coordinate 0 and outer X to 1. · OAI.Nagata.W18.nestedToBivariate

NestedTracialMatrices structure

Raw nested matrix embeddings, with density stated for their represented algebra vectors. No Hilbert coefficient identity is part of this data. · OAI.KadisonSimilarity.NestedTracialMatrices

nesting def

Nesting of idempotents; distinct from edge inclusion. · OAI.TwoWayComplementation.Diagram.nesting

net def

Multiplier from the eight rows (chronologically right to left). · OAI.PowerSaving.Cluster.net

NetEmits def

Exact, syntactic network emission. Pack budgets are internal certificates, not additional generator advice. · OAI.ExactQuantumFactoring.NetworkEmission.NetEmits

netMap def

Send a point in the working ball to the corresponding limiting net point. Outside that ball the map takes the base-point value. · OAI.RegularPointCoordinates.MovingRescalingNetFamily.netMap

netMap def

Send a point in the working ball to the corresponding limiting net point. Outside that ball the map takes the base-point value. · OAI.RegularPointCoordinates.RescalingNetFamily.netMap

netProjectionSupport def

A measurable common support enclosure indexed by a finite input net. · OAI.SubsphereRegression.netProjectionSupport

Network structure

An oriented edge enumeration; only the associated undirected unit-edge simple graph is used for distances. · OAI.ForestSpace.Diamond.Network

Network structure

A finite-path network with labelled entrances and exits at both boundaries. · OAI.TwoWayComplementation.Network

Neutral inductive

The variable-headed spines used by the manuscript. · OAI.PureTypeSystem.Neutral

neutralDiagonalOppositeHom def

The opposite representation matches the right action on lattices. · OAI.DukePrimeDegree.neutralDiagonalOppositeHom

neutralJitterReal def

A bounded smooth periodic jitter that is exactly affine on the fixed large good arc. The cutoff and good arc do not depend on the slope. · OAI.ThreeTorus.neutralJitterReal

NewAt def

The unique original successor where an element first appears. · OAI.PartitionConsistency.ConservativeMonoids.CellTower.NewAt

newComponent def

Its separated new-facet label has only one orbit; this identifies the ENTIRE new facet boundary, in an arbitrary sewn global occurrence diagram. · OAI.IntegralCharacterVarieties.FiniteCycles.Polygon.newComponent

newCoord def

The second coordinate of a point on a replacement line. · OAI.KaplanskyCounterexample.FiniteGeometry.DirectionFrame.newCoord

newLeaf def

The single distinguished newly added replica position. · OAI.DilutedSpinGlass.PrescribedTree.newLeaf

newPath def

The new path shares just its prescribed prefix, even for repeated values. · OAI.DilutedSpinGlass.PrescribedTree.newPath

newSides def

The new facet's entire boundary side set, not just an embedded subset, is exactly the given polygon. This makes its unique boundary equation available. · OAI.IntegralCharacterVarieties.FiniteCycles.Polygon.newSides

newton def

P upper from monic Newton basis · OAI.PowerSaving.Spectral.newton

newtonKernel def

The Newton kernel, including its harmless diagonal convention. · OAI.HenonLaneEmden.newtonKernel

newtonTensor def

The penultimate Newton tensor, defined polynomially, not using an inverse. · OAI.AffineBernstein.newtonTensor

next def

A single uniform ghost extends every partially constructed homotopy by a whole CW dimension, even if there are infinitely many cells in that dimension. · OAI.GroupRingTopology.Cellular.PartialHomotopy.next

next def

Extend a partial lift across all cells of the next dimension. · OAI.GroupRingTopology.Cellular.PartialLift.next

next def

One complete recursive level, with actual single-coordinate leaf noise. · OAI.MaxCutGames.Gadget.Stage.next

next def

One concrete finite stage, with the original anchor preserved. · OAI.ReflexiveFixedPoints.AnchoredCandidateContext.next

next def

The recursion step is defined even on bad predecessor data; the bad branch is never used in the well-founded construction. · OAI.SeparableQuotient.CoherentClosures.next

next abbrev

The actual successor map of the diagram. · OAI.Thomason.Construction.TopologicalDeformation.Sequential.next

next def

The edge reversal followed by the unique turn at an unmarked degree-two vertex. At marked vertices the turn fixes all outgoing darts. · OAI.TorsionFreeZeroDivisors.ChainSuppression.next

next def

One complete recursive level, with actual single-coordinate leaf noise. · OAI.UniqueGamesTheorem.Gadget.Stage.next

nextBlockRank def

The image dimension of the actual oriented child restriction map. · OAI.MaxCutGames.Quadratic.nextBlockRank

nextBlockRank def

The image dimension of the actual oriented child restriction map. · OAI.UniqueGamesTheorem.Quadratic.nextBlockRank

nextBudget def

The next budget is fixed by the full history, including discarded maps. · OAI.ReflexiveFixedPoints.CandidateContext.nextBudget

NextCollision structure

A finite collision datum whose existence is proved from the actual half-plane geometry and the countable unfolded-vertex exception. · OAI.TriangularBilliards.NextCollision

nextLeft def

Move 0 is left, move 1 is stationary, and move 2 is right. · OAI.ForcedComputation.Lattice.nextLeft

nextNode def

The canonical identification of next-level nodes with the actual extension. · OAI.ReflexiveFixedPoints.FrontierTower.nextNode

nextOrdinal def

The globally fresh zero-based label before a candidate is chosen. · OAI.ReflexiveFixedPoints.CandidateContext.nextOrdinal

nextSet def

Insert a chosen unused coordinate while there are coordinates remaining. · OAI.MaxCutGames.Foundations.Repetition.SelectionSequence.nextSet

nextSet def

Insert a chosen unused coordinate while there are coordinates remaining. · OAI.UniqueGamesTheorem.Foundations.Repetition.SelectionSequence.nextSet

nextSigned def

The direction of a step is given by the signed letter. Non-carrier values are immaterial and are defined to fix the vertex. · OAI.TorsionFreeZeroDivisors.Types.nextSigned

nextState def

A state of the alternating conditional cluster resampling chain. · OAI.HyperedgeComparison.nextState

NilpotentDynkinExpansionInput def

The bounded finite Dynkin expansion, specialized to the actual tangent Lie algebra and its intrinsic exponential. No metric growth estimate is part of this published hypothesis. · OAI.PolycyclicRecognition.NilpotentDynkinExpansionInput

NilpotentExponentialHaarInput def

The part of the nilpotent exponential-coordinate theorem needed for Haar volume. The hypotheses concern the actual tangent Lie algebra of the group. · OAI.PolycyclicRecognition.NilpotentExponentialHaarInput

nilpotentFactorToRotation def

The actual nilpotent kernel embeds with its original multiplication. · OAI.PolycyclicRecognition.ComplexWeightFactorModel.nilpotentFactorToRotation

NilpotentGlobalExponentialChartInput def

Only the global topological chart, with no measure compatibility. · OAI.PolycyclicRecognition.NilpotentGlobalExponentialChartInput

NilpotentIdealNormalityInput def

Exact connected embedded nilpotent specialization of Lee's ideal criterion. All Lie algebras here are the actual tangent Lie algebras. · OAI.PolycyclicRecognition.NilpotentIdealNormalityInput

NilpotentLieExistenceInput def

The nilpotent specialization of Lie correspondence in exponential polynomial coordinates. · OAI.PolycyclicRecognition.NilpotentLieExistenceInput

NilpotentLieIntegrationInput def

Nilpotent-domain specialization of Lie's integration theorem and naturality of the exponential. · OAI.PolycyclicRecognition.NilpotentLieIntegrationInput

NilpotentLieModel structure

Only the finite-dimensional simply connected integration data. Haar measure and intrinsic exponentials are obtained from their separate input. · OAI.PolycyclicRecognition.NilpotentLieModel

NilpotentSmoothIntegrationInput def

The still-undischarged existence assertion of Lee (2013), Theorem 20.19, in precisely the nilpotent-source specialization used in the application. · OAI.PolycyclicRecognition.NilpotentSmoothIntegrationInput

nilradicalLinearAction def

The restricted linear representation has the same compact parameter group. · OAI.PolycyclicRecognition.ComplexTriangularAdjoint.nilradicalLinearAction

nilradicalRotation def

Restrict the real rotations to the intrinsic nilpotent adjoint kernel. · OAI.PolycyclicRecognition.ComplexTriangularAdjoint.nilradicalRotation

nilradicalRotations def

A fixed choice of the integrated compact action. · OAI.PolycyclicRecognition.nilradicalRotations

nineDisplacement def

Positive arithmetic-progression displacements of total Δ. · OAI.Nagata.W06.nineDisplacement

nineThetaSection def

The actual nine-theta product as a degree-nine section. · OAI.Nagata.CoefficientSpaces.nineThetaSection

NMachineOn structure

A nondeterministic automaton on an arbitrary state type. · OAI.OneWayLiveness.NMachineOn

nnInternalEnds def

Internal ends at which both incident layers have type N (false). · OAI.Problem335.BalancedSchedule.nnInternalEnds

nnz def

Number of supported scalar positions. · OAI.ExactFourier.Triangular.nnz

NoAdjacentBranchDepths def

Regular depth assignments imply this no-adjacent-depth condition once eta L > 1. It is precisely the geometric premise of shifted charging. · OAI.DilutedSpinGlass.PrescribedTree.NoAdjacentBranchDepths

noChangeSplitMass def

All second assignments agree with the first assignments, retaining the necessary lower tail restrictions on the two remaining sets. · OAI.JointDickman.noChangeSplitMass

NoCollision def

Row-column noncollision: at most one source cell in any row can land in any destination column. · OAI.CoordinateSweeps.YoungCorner.NoCollision

NoCompiledInputDecider def

No total algorithm on the finite source descriptions decides the given observation for all valid compiled inputs. · OAI.ForcedComputation.NoCompiledInputDecider

NoCornerInCoordinates def

No corner in every finite slope of the horizontal coordinate chart. · OAI.GammaFPP.Analytic.NoCornerInCoordinates

NoCornerWedge def

The slope wedge used by the manuscript's probabilistic argument. · OAI.GammaFPP.Analytic.NoCornerWedge

nodalMeasure def

Hausdorff measure for the path distance of the actual Riemannian metric, not the metric inherited from any ambient embedding. · OAI.YauCounterexamples.nodalMeasure

Node def

Actual ordered-tree nodes, with a distinct trivial leaf at every empty corner word. Coincident map poles are not identified as tree nodes. · OAI.FKCRT.Inventory.CoreTree.Node

Node abbrev

The connector presentation uses two directed copies of each undirected edge; duplication does not change any reachable starred vertex. Nonedges are isolated connector nodes. · OAI.HyperedgeComparison.Site.Node

Node abbrev

Nodes at which a depth-d router still makes a decision. · OAI.Problem310.FiniteTableModel.Node

node def

The pairwise node of components i and j. · OAI.Nagata.W06.LineArrangement.node

node def

Node-wise assembly of genuine edge labels. · OAI.TraceReconstruction.OccupiedParityTree.Labels.node

nodeCountAtDepth def

Literal count of nodes at one remaining physical depth. · OAI.EditApproximation.DependencyExpansion.nodeCountAtDepth

nodeCountAtOrAbove def

Literal count of nodes whose remaining physical depth is at least floor. Descendants are inspected even when the current node fails the test; pruning below the threshold is a consequence of Valid. · OAI.EditApproximation.DependencyExpansion.nodeCountAtOrAbove

nodeCountThroughDescent def

All nodes reached with physical descent at most j, including those reached through earlier-index edges that themselves decrease depth. · OAI.EditApproximation.DependencyExpansion.nodeCountThroughDescent

nodeEquiv def

The literal preorder indexing is an equivalence, including the root. · OAI.FKCRT.Inventory.CoreTree.nodeEquiv

noDefaultEvent def

No default occurs on the actual center path. Terminal coordinates do not enter this event, but are retained in the probability space. · OAI.Problem310.CenterFailureBound.noDefaultEvent

nodeHistoryBudget def

A grid-independent budget for all leaves and history colors used in the aligned two-copy experiment of a fixed topology. · OAI.DilutedSpinGlass.ReducedTopology.nodeHistoryBudget

NodeKey abbrev

Each occurrence carries its complete ancestral path. Equal labels under separate parents are never identified or memoized. · OAI.ExactQuantumFactoring.DataProducer.NodeKey

nodeLabel def

The actual anchor images labelling every node of the tree. · OAI.ReflexiveFixedPoints.SwitchingTreeData.nodeLabel

NodeMachine structure

A bit-level finite-state controller. Both transition functions are literal Boolean networks; this structure does not grant any classical computation oracle. · OAI.ExactQuantumFactoring.NodeMachine

nodeNamed def

The clamp with the manuscript's consistent atom-name tie rule. · OAI.PlanarL1.Interpolation.nodeNamed

nodeParity def

Boolean parity, in the convention used by ModeIncidence. · OAI.Problem348.Construction.nodeParity

nodePathIndex def

false descends left, true descends right. · OAI.Ostmann.nodePathIndex

nodePoint def

Same-code positive mesh, with the omitted root still present at time zero. · OAI.FKCRT.Inventory.CoreTree.nodePoint

nodePotential def

One step of the actual recursive bad-node potential. · OAI.LeanBlast.SecondKahnKalai.nodePotential

nodeRow def

One row at a node of height h+1. · OAI.TreeEdit.BinaryLower.FiniteTree.nodeRow

nodeShiftBudget def

Topology-dependent quadratic energy budget in the depth continuity bound. · OAI.DilutedSpinGlass.UniversalDictionary.nodeShiftBudget

nodeValue def

The exact parent/tentative clamp in the source: U=max parent A, L=min parent B, and F=min U (max L T). · OAI.PlanarL1.Interpolation.nodeValue

nodeWord def

Assemble a binary node without changing either operand, even if the store destination aliases an operand. The buffer and temporary are cleared. · OAI.ParityWL.Complexity.nodeWord

nodeWord def

A row is the ordered concatenation of the m child words. At a leaf the word consists of its single tagged state symbol. · OAI.TreeEdit.BinaryLower.FiniteTree.nodeWord

noDummyEquiv def

Omitting all dummy darts recovers exactly the original dart set. · OAI.MaxCutGames.Foundations.PCP.DegreeReplacement.noDummyEquiv

noDummyEquiv def

Omitting all dummy darts recovers exactly the original dart set. · OAI.UniqueGamesTheorem.Foundations.PCP.DegreeReplacement.noDummyEquiv

NoExactOverlaps def

Absence of equality between complete affine maps of distinct finite words. · OAI.EntropyRateDimension.Extensions.NoExactOverlaps

NoExtraEuclideanFactor def

The ball-map form of the no-(n+1)-Euclidean condition. · OAI.RegularPointCoordinates.NoExtraEuclideanFactor

Noise abbrev

A complete noise assignment. Bounds and independence are imposed on the actual probability space later, not assumed properties of the output. · OAI.PlanarL1.Columns.Model.Point.RadialTree.Noise

noise def

Original finite noise choices, pushed through the actual quotient map. · OAI.MaxCutGames.Gadget.StageQuotient.noise

noise def

Ordinary Boolean noise in its exact Walsh multiplier representation. Range/mean preservation must be proved, not imposed as assumptions. · OAI.OptimalMaxCut.Analytic.noise

noise def

The biased noise operator, defined by its Fourier multiplier. · OAI.Problem313.BiasedFourier.noise

noise def

Original finite noise choices, pushed through the actual quotient map. · OAI.UniqueGamesTheorem.Gadget.StageQuotient.noise

noiseCount def

R_Γ from lem:elementary-entry-tests. · OAI.PixtonChow.StableGraph.noiseCount

noiseDenominator def

A positive rational has numerator at least one, so its reciprocal denominator is no larger than the rational itself. Adding two also ensures the noise parameter is at most one half for every input. · OAI.MaxCutGames.Foundations.Hastad.SourceNoiseParameter.noiseDenominator

noiseDenominator def

A positive rational has numerator at least one, so its reciprocal denominator is no larger than the rational itself. Adding two also ensures the noise parameter is at most one half for every input. · OAI.UniqueGamesTheorem.Foundations.Hastad.SourceNoiseParameter.noiseDenominator

noiseEigenvalue def

The probability of the event S v = 0, with the supplied finite weights. · OAI.MaxCutGames.Fourier.MatrixNoise.noiseEigenvalue

noiseEigenvalue def

The probability of the event S v = 0, with the supplied finite weights. · OAI.UniqueGamesTheorem.Fourier.MatrixNoise.noiseEigenvalue

noiseParameterShift def

The polar shear preserves the first coordinate and is its own inverse. · OAI.MaxCutGames.Quadratic.noiseParameterShift

noiseParameterShift def

The polar shear preserves the first coordinate and is its own inverse. · OAI.UniqueGamesTheorem.Quadratic.noiseParameterShift

NoLowCircular def

Absence of a low separating tip is intrinsically circular: reversing the listed chord endpoints does not change the exclusion test. · OAI.PlanarL1.Columns.Model.Field.NoLowCircular

NoLowTip def

Complement of the main procedure's barrier-drop exclusion. Both endpoint thresholds are tested, exactly as in pack:barrier and pack:retained-data. · OAI.PlanarL1.Columns.Model.Field.NoLowTip

NonamenableWitness def

A uniformly 101-bounded nonunitarizable representation on a separable complete complex Hilbert space, with its universe explicit. · OAI.Dixmier.NonamenableWitness

nonanchorClass def

Column-class labels for the non-anchor induced submatrix. The dummy label is irrelevant because dummy columns are treated separately. · OAI.Problem348.Construction.nonanchorClass

NonanchorPosition abbrev

The two kinds of non-anchor positions, without their outer sum tag. · OAI.Problem348.Construction.NonanchorPosition

nonbacktracking def

The copy indexed by i receives all transitions except the one with the same index. · OAI.TwoPointCorrelations.nonbacktracking

nonconstantCoefficient def

The constant-term deletion of a polynomial. · OAI.TraceReconstruction.nonconstantCoefficient

Noncrossing def

No two links have four alternating, distinct endpoints in cyclic order. · OAI.PlanarL1.ColumnOrder.Noncrossing

NondegenerateCoordinates abbrev

A nondegenerate simplex with its barycentric coordinates. · OAI.Thomason.Construction.RealizationPrism.NondegenerateCoordinates

NondegeneratePoints abbrev

The disjoint union of the parameter spaces of nondegenerate simplices. · OAI.Thomason.Construction.RealizationPrism.NondegeneratePoints

nonempty def

a ≠ ∅, stated as existence of a member. · OAI.PartitionConsistency.SetLanguage.nonempty

nonemptyFamily def

A graph F coding a family of nonempty sets indexed by ordinal η. · OAI.PartitionConsistency.SetLanguage.nonemptyFamily

nonemptyFinColumnFamily def

A nonempty stage gives the finite amplification frame without any additional existence hypothesis. · OAI.KadisonSimilarity.NestedTracialMatrices.nonemptyFinColumnFamily

NoNewOldDivisors def

The no-new-divisors alternative at a successor stage. All divisibility statements are in the ambient final monoid. · OAI.PartitionConsistency.DiagramOrder.NoNewOldDivisors

NonexpansiveOn def

Nonexpansiveness is measured in the original ambient norm. · OAI.ReflexiveFixedPoints.NonexpansiveOn

nongenericFraction def

The actual uniform fraction of nongeneric rank-r binary subspaces. · OAI.MaxCutGames.Quadratic.nongenericFraction

nongenericFraction def

The actual uniform fraction of nongeneric rank-r binary subspaces. · OAI.UniqueGamesTheorem.Quadratic.nongenericFraction

noninteractingPressure def

Deterministic reference obtained by removing the quadratic interaction. · OAI.InvariantIsing.noninteractingPressure

nonlightFactor def

Product outside the light-line expectation; zero validity is handled separately, never by interpreting a divergent inverse-gamma moment. · OAI.CoordinateSweeps.Grid.Holes.nonlightFactor

nonlinearBound def

Upper bound for the transformed nonlinearity, c = .271. · OAI.StationaryNS.nonlinearBound

nonlinearPacket def

Actual nonlinear angular coefficients are glued by their deviations from roundness. This finite sum is smooth without differentiating a discontinuous angular selector. On disjoint packet supports it is exactly the Berger model. · OAI.HarmonicCounterexample.FiniteControl.SmoothWord.nonlinearPacket

nonnegativeAugmentation def

The augmentation for a nonnegatively supported integer grading is actual degree-zero projection. · OAI.KLInvariance.Graded.nonnegativeAugmentation

nonnegativeGain def

The nonnegative symmetric gain in the original normal-sphere variables. · OAI.BoltzmannNonuniqueness.nonnegativeGain

nonnegativePart def

Laurent polynomials with no negative powers, viewed as a k-subalgebra. · OAI.StableCoordinate.LaurentWeightObstruction.nonnegativePart

NonnegCoeffs def

Coefficientwise nonnegativity, used only for the positive centered expansion. · OAI.CoordinateSweeps.MomentExpansion.NonnegCoeffs

nonnegToExtendedReal def

ENNReal, used for nonnegative local-ring values, embedded in the extended real additive group used on the fraction field. · OAI.CartierSections.nonnegToExtendedReal

nonpositiveResolutionBarIso def

Integration API for Q_X: the native integer-derived functor agrees naturally with the genuine bar-derived functor after chainToIntegerDerived. · OAI.LittleFinitistic.BimoduleTotal.nonpositiveResolutionBarIso

nonpositiveResolutionPowerIso def

Exact source-style F^r applied to a native degree-zero module, represented by the genuine Section 6 indexed multibar. All comparison data is constructed. · OAI.LittleFinitistic.BimoduleTotal.nonpositiveResolutionPowerIso

nonpositiveTotalFunctorIso def

Exact comparison of the ordinary resolution's finite list with the native interval. · OAI.LittleFinitistic.BimoduleTotalPresentation.nonpositiveTotalFunctorIso

NonrootNode abbrev

Every nonroot node, retaining its actual positive level. · OAI.ReflexiveFixedPoints.OrderedTree.NonrootNode

NonsingularAction structure

A measurable group action preserving the measure class. · OAI.KadisonKastler.NonsingularAction

NonuniquenessStatement def

Two global solutions of one datum, differing on a common initial interval. · OAI.BoltzmannNonuniqueness.NonuniquenessStatement

NonvanishingFlag def

For the actual second oblique chain, the bases are reordered relative to the sorted complete jets. The orientation is immaterial for a pencil ratio. · OAI.CriticalHoneycomb.FiniteFunctional.StripAsymptotic.NonvanishingFlag

NonzeroBlock abbrev

The uniform noise space after conditioning the perturbation to be nonzero. · OAI.MaxCutGames.Quadratic.NonzeroBlock

NonzeroBlock abbrev

The uniform noise space after conditioning the perturbation to be nonzero. · OAI.UniqueGamesTheorem.Quadratic.NonzeroBlock

nonzeroBlockChangeProbability def

Exact uniform expectation of the nonlinear-change indicator. · OAI.MaxCutGames.Quadratic.nonzeroBlockChangeProbability

nonzeroBlockChangeProbability def

Exact uniform expectation of the nonlinear-change indicator. · OAI.UniqueGamesTheorem.Quadratic.nonzeroBlockChangeProbability

nonzeroBundle def

The ordinary total space with its entire zero section removed. · OAI.Kaplansky.nonzeroBundle

nonzeroEquiv def

Every nonzero vector lies on exactly one of these parametrized lines. · OAI.KaplanskyCounterexample.IncidenceDirections.nonzeroEquiv

nonzeroFiberEquiv def

The explicit algebraic nonzero-fiber calculation, valid over any field. · OAI.StableCoordinate.NonzeroFiber.nonzeroFiberEquiv

NonzeroHomogeneousForm structure

A nonzero degree-d homogeneous ternary complex polynomial. Nonreduced and reducible equations are allowed. · OAI.Nagata.W16.NonzeroHomogeneousForm

nonzeroProgressions def

Actual ordered nonzero-step progressions in a finite cyclic group. · OAI.QuantitativeVanDerWaerden.SparsePerturbation.nonzeroProgressions

NoPairTies def

No two affine scores agree at the point. · OAI.Problem358.TripleTieAvoidance.NoPairTies

noPreservationSubsetMatrix def

The subset adjacency occurring at a cut with no preservation letter. · OAI.KadisonKastler.noPreservationSubsetMatrix

norm def

Weighted support norm. · OAI.CoboundaryExpanders.Complex.norm

norm def

The source's weighted support norm, not the unweighted Hamming norm. · OAI.CoboundaryExpanders.Complex.norm

normal def

Normalization of a cleanup head, with or without a left boundary. · OAI.FiniteAlgebraicEnvelopes.Compiler.Cleanup.normal

normal def

The source algorithm, with the partial call separated as f. Its actual computable domain/realization is established at the program boundary. · OAI.FiniteAlgebraicEnvelopes.Compiler.Word.normal

normalAmplitude def

Applying the physical normal operator to each tangential monomial. · OAI.ElasticityBoundaryRecursion.normalAmplitude

normalBase def

A canonical basepoint of the affine equation inner n x + c = 0. · OAI.Problem358.IntrinsicSurface.normalBase

NormalCentralAverage structure

The part of a center-valued trace used by the scalar trace construction. · OAI.BoundedHochschild.KadisonRingrose.NormalCentralAverage

normalChange def

Restrict a full frame change to the three normal vectors. · OAI.PositiveEinsteinFour.Geometry.normalChange

normalChart def

The normal product chart, with the tangential variable first as in a moving-halfspace disintegration. · OAI.Problem358.HouseholderCoordinates.normalChart

normalCoefficient def

A vector functional restricted to the concrete algebra. · OAI.KadisonSimilarity.normalCoefficient

normalCoefficientFamily def

The actual finite normal polynomial Σ_{j≤J} q_j(U) W^j. · OAI.Nagata.W18.normalCoefficientFamily

normalCon def

Equality of reduced traces is a monoid congruence on signed words. · OAI.EilenbergGanea.TraceWords.normalCon

normalCounts def

Local gates are moved to the right by rotating the product axes; supports are unchanged, so a disjoint physical layer yields one reflection layer. · OAI.QAC.normalCounts

normalCurvatureDerivative def

The derivative field uses the metric's actual covariant derivatives. · OAI.PositiveEinsteinFour.Geometry.normalCurvatureDerivative

normalDerivative def

The normal pairing in a derivative layer, including equal coordinates. · OAI.Problem335.FactorialExpansion.normalDerivative

normalDeviation def

The curvature deviation in the normal basis I_s q. · OAI.PositiveEinsteinFour.Angular.normalDeviation

normalDisplacement def

The displacement at each actual tuple point, in the actual normal multiplier fibre D(9,L³). L is the degree-three multiplier; the cubic/normal-bundle identification is a separate input. · OAI.Nagata.W06.TorusConfiguration.normalDisplacement

normalEndpointCount def

Number of endpoints at which both adjacent pairing types are normal. · OAI.Problem335.Pairings.normalEndpointCount

normalEquiv def

Full orthogonal normal/tangent coordinates for an arbitrary nonzero normal. · OAI.Problem358.TangentNormalCoordinates.normalEquiv

normalEvaluation def

Evaluate <R(I_i q,q)q,I_j q> as a linear functional on four-tensors. · OAI.PositiveEinsteinFour.Angular.normalEvaluation

normalExtensionSecondPageIso def

The canonical second page uses the derived quotient action on normal subgroup homology, independent of the chosen ambient resolution. · OAI.PolycyclicRecognition.normalExtensionSecondPageIso

normalFamilyArgument def

Actual argument of the inverse normal chart in parameter and fiber variables. · OAI.Nagata.Workers.W28.normalFamilyArgument

NormalFiniteTrace structure

The constructed normalized faithful normal trace. · OAI.KadisonSimilarity.NormalFiniteTrace

normalForm def

Choice of the unique full beta normal form when it exists. The fallback is irrelevant on legal syntax under the standing system-wide WN hypothesis. · OAI.PureTypeSystem.Expr.normalForm

normalFormEquiv def

The underlying normal-form coordinates are bijective. · OAI.PolycyclicRecognition.GroupExtensionSection.normalFormEquiv

normalFunctionalSpace def

Normal functionals, with their operator-dual norm. · OAI.KadisonSimilarity.normalFunctionalSpace

normalGeometricMass def

Geometric first/second-moment input, before normalization, for normal pairings. · OAI.Problem335.LocalMoments.normalGeometricMass

normalGNSLinear def

The representation as a continuous linear map. · OAI.BoundedHochschild.KadisonRingrose.normalGNSLinear

normalInductionTensorIso def

This is an isomorphism of the actual ambient group representations. · OAI.PolycyclicRecognition.normalInductionTensorIso

normalization def

The full linearization automorphism, turning H+p w into an equation linear in the slot formerly called F, while fixing p. · OAI.StableCoordinate.Linearization.normalization

normalization def

The nondegenerate coordinates of an actual realization point. · OAI.Thomason.Construction.RealizationPrism.normalization

normalizationCocone def

Nondegenerate coordinates form a cocone of sets over all realization simplices. · OAI.Thomason.Construction.RealizationPrism.normalizationCocone

normalizationFactor def

The positive covolume-normalizing scalar. · OAI.DukePrimeDegree.normalizationFactor

normalizationQuotientEquiv def

Normalize the shifted equation to the monic linear equation F-u+p*w. · OAI.StableCoordinate.Stabilization.normalizationQuotientEquiv

normalize def

Normalizing a nonzero isotropic vector gives a legitimate unit representative. · OAI.ArnoldCounterexample.Quadric.normalize

normalize def

Canonicalize a binary word, charging a linear-growth bit fold. · OAI.ExactQuantumFactoring.BitStackProgram.Procedure.normalize

normalize def

Normalization of nonnegative counts. Positivity is proved before this construction is used to form the uniform present-star law. · OAI.HyperbolicObstruction.FiniteLaw.normalize

normalize def

Normalize an arbitrary lift of a recorded occurrence to its primitive phase. · OAI.Superstring.Hierarchical.Layer.normalize

normalize def

Only the period residue of a recipient offset is stored. · OAI.Superstring.Hierarchical.Layer.Record.normalize

normalize def

The basic interval obtained by applying the inverse chart of I to K. · OAI.ThompsonNonamenability.BasicInterval.normalize

normalizeAtZero def

Extend the values on ℂ* by zero at the omitted point. · OAI.Nagata.W08.normalizeAtZero

normalizeBoundaryGenerators def

This changes all side and frame coordinates, so it respects every named quotient at every vertex, not just a list of boundary conjugacy classes. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.normalizeBoundaryGenerators

normalizeBoundarySolution def

A full solution in canonical boundary path coordinates. It is constructed from any old solution, uniformly over the full coefficient ring. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.normalizeBoundarySolution

normalizeCircle def

Circle normalization chosen compatibly with quaternion normalization. · OAI.EilenbergGanea.normalizeCircle

Normalized def

The exact local normalization needed for junction gluing. At zero-mass states no conditional probability is required. · OAI.BoundedTreewidthL1.TreeMarkov.Normalized

normalized def

Every cap is normalized exactly, with no rotational-invariance assumption. · OAI.HenonLaneEmden.CapWeights.normalized

normalized def

A chart normalized on its identified quotient. · OAI.IntegralCharacterVarieties.ExactSequenceChart.Chart.normalized

normalized def

Normalized coefficients after evaluating all small prime variables. · OAI.Ostmann.PolynomialGiantRows.normalized

normalizedAWMap abbrev

Typed form of the explicit normalized AW map. · OAI.Thomason.Construction.SimplexAtomsInput.normalizedAWMap

normalizedBallSlice def

The ball-restricted chart integral with factor 1 / (W(v) * ‖v-p‖). Identifying this chart factor with the collision-plane measure is a separate change-of-variables statement. Degenerate parameters retain the value infinity. · OAI.BoltzmannNonuniqueness.GeometricSlice.normalizedBallSlice

normalizedBasis def

The special-linear matrix of the normalized column lattice. · OAI.DukePrimeDegree.normalizedBasis

normalizedBlockNorm def

The normalized Weyl norm, written without a choice of eigenvectors. · OAI.PositiveEinsteinFour.Geometry.normalizedBlockNorm

normalizedBlowupChart def

The genuine affine blowup-chart algebra: adjoin the original eighteen section ratios to the whole normalization, all in the original function field. This definition is not an interface assuming a Cartier model. · OAI.ExplicitCone.normalizedBlowupChart

normalizedBodyKernel def

Normalized restrictions of a jointly measurable family form a kernel. No normalization assertion is made at zero or infinite mass. · OAI.Problem358.AffineSlice.normalizedBodyKernel

normalizedCell def

The literal fixed cell of bounds.tex. · OAI.AffineBernstein.normalizedCell

normalizedCellDomain def

The open positive neighbourhood used for differentiating support functions. · OAI.AffineBernstein.normalizedCellDomain

normalizedCellLaw def

The probability law obtained by conditioning a measure on a positive finite cell. · OAI.Problem358.normalizedCellLaw

normalizedCenters def

A finite, endpoint-safe index type for major-arc integration. · OAI.Problem337.MinorArc.normalizedCenters

normalizedChosenDescription def

A fixed normalized witness determined by the visible table and row advice. All remaining inputs are the fixed normalization functional and proofs. · OAI.MaxCutGames.Inverse.RowErasureMatrix.normalizedChosenDescription

normalizedChosenDescription def

A fixed normalized witness determined by the visible table and row advice. All remaining inputs are the fixed normalization functional and proofs. · OAI.UniqueGamesTheorem.Inverse.RowErasureMatrix.normalizedChosenDescription

normalizedCone def

The WHOLE integral closure of the literal section-generated cone in its function field; no smaller radical subalgebra is substituted. · OAI.ExplicitCone.normalizedCone

normalizedConfigInclusion def

Include the normalization hyperplane into the unrestricted configuration space. · OAI.Problem358.CellGeometry.normalizedConfigInclusion

normalizedConstantSection def

A genuine constant section on C*, represented by zero extension at zero. · OAI.Nagata.Workers.W10.normalizedConstantSection

normalizedCoordinates def

Normalized top coordinates, using first a translation, then the slope shear, then the two independent dilations. · OAI.LipschitzHilbert.SlopeBox.normalizedCoordinates

normalizedCoordinates def

The normalized coordinate map, with its value at the center removed. · OAI.RegularPointCoordinates.normalizedCoordinates

normalizedCornerGeometry def

The normalized tracial representation on pL²(P)p, with the scalar chosen from the actual trace of p. · OAI.KadisonSimilarity.TracialCornerGeometry.normalizedCornerGeometry

normalizedCornerGNSInclusion def

A normalized corner vector realizes the state on its GNS space. · OAI.WeakPureInfiniteness.normalizedCornerGNSInclusion

normalizedCornerVector def

Rescale the ordinary corner vectors so that their inner product is the normalized corner trace. · OAI.KadisonSimilarity.TracialCornerGeometry.normalizedCornerVector

NormalizedCounterexample def

A strict directionwise half-area bound for the same regular tetrahedron. · OAI.TriangularCovering.NormalizedCounterexample

normalizedCovector def

The covector field uses the dual coordinate change. · OAI.RegularPointCoordinates.normalizedCovector

normalizedCurvePoint def

Actual affine chart coordinates of a homogeneous analytic parametrization. · OAI.Nagata.Workers.W28.normalizedCurvePoint

normalizedDensityKernel def

The normalized sections form a measurable kernel, even before probability assumptions are imposed on their total masses. · OAI.Problem358.normalizedDensityKernel

normalizedDensityMeasure def

A density section normalized to have total mass one. · OAI.Problem358.normalizedDensityMeasure

normalizedDescription def

The actual normalized description, chosen using only the left observation. · OAI.MaxCutGames.Decoder.SelectedPolicies.normalizedDescription

normalizedDescription def

The actual normalized description, chosen using only the left observation. · OAI.UniqueGamesTheorem.Decoder.SelectedPolicies.normalizedDescription

normalizedDihedralWordMap def

The normalized algebraic word map whose Hilbert extension is isometric. · OAI.KadisonSimilarity.normalizedDihedralWordMap

normalizedDilation def

The Jacobian factor makes spatial dilation preserve the physical norm. · OAI.ContinuumCoulomb.normalizedDilation

NormalizedDrawing structure

A convenient subdivision of a normalized drawing. Avoiding subdivision knots at crossings is additional presentation data, obtained by the normalization theorem. · OAI.Paper170.NormalizedDrawing

normalizedEndpointMeasure def

Probability normalization on the endpoint subtype. · OAI.PolycyclicRecognition.normalizedEndpointMeasure

normalizedEntry def

Cramer's numerators are computed by the staged division-free algorithm. · OAI.RationalHitting.ExecutableGenerator.normalizedEntry

normalizedEquiv def

The invertible normalized cell-mass Jacobian. This is the continuous-linear-equivalence interface needed by the implicit function theorem. Its existence makes no assertion of a uniform bound on the inverse. · OAI.Problem358.CellLaplacian.normalizedEquiv

normalizedError def

A single error statistic for the actual table, scaled by its nonrandom expected star count. The leaf mean, not a fresh independent table, supplies the normalizing-total estimate. · OAI.HyperbolicObstruction.StarModel.normalizedError

normalizedExtensionSection def

A normalized section exists for every surjective group extension. · OAI.PolycyclicRecognition.normalizedExtensionSection

normalizedFactorTrace def

The constructed faithful normalized trace on the original factor. · OAI.Generator.normalizedFactorTrace

normalizedFamilyCycle def

Actual locally finite cycle for an arbitrary countable family of compact-source cycles. · OAI.CoarseAssembly.Analytic.normalizedFamilyCycle

NormalizedFiniteBallBound def

The normalization is by the cardinality of the entire finite set. · OAI.Falconer.NormalizedFiniteBallBound

normalizedFiniteSignSum def

The usual variance-one normalization of the finite sign sum. · OAI.KadisonKastler.normalizedFiniteSignSum

normalizedFrame def

The chosen polynomial frame has exactly the original frame at parameter zero. · OAI.StableCoordinate.NormalizedDeterminantLift.normalizedFrame

normalizedFunction def

Center-preserving horizontal normalization and positive vertical scaling. · OAI.AffineBernstein.normalizedFunction

normalizedGenerator def

The normalized generator s^{-1} a_h on L=E_0 in Q. · OAI.LittleFinitistic.QuadraticEncoding.normalizedGenerator

normalizedGroundProjection abbrev

Precisely Π/Tr Π for the orthogonal projection on the entire bosonic ground space. The nonzero condition is exactly the domain of normalization, not a finite-rank assumption. · OAI.HardSphere.normalizedGroundProjection

normalizedGroupParameters def

Normalized Lie data whose fixed Dynkin product satisfies the group laws. · OAI.PolycyclicRecognition.normalizedGroupParameters

NormalizedHarmonicTest structure

One normalized harmonic test on a measured almost-Euclidean ball. · OAI.RegularPointCoordinates.NormalizedHarmonicTest

NormalizedHermitianTuple structure

A normalized tuple with the adjoint identity proved for its displayed reverse maps. No existence or topological obstruction is assumed here. · OAI.Kaplansky.NormalizedHermitianTuple

normalizedHilbertSignSum def

The variance-one normalized Hilbert-space sign sum. · OAI.KadisonKastler.normalizedHilbertSignSum

normalizedIntegral def

The normalized primitive at a fixed time, with its linear dependence on all periodic input data made explicit. · OAI.ClosedSurfaceR4.PeriodicIntegralOperator.normalizedIntegral

normalizedInteriorConvolution def

Normalized interior convolution from re:convolution-decay. · OAI.RegularPointCoordinates.normalizedInteriorConvolution

normalizedKernel def

The kernel normalized for counting measure on ZMod q. · OAI.Problem337.CyclicSmoothing.normalizedKernel

NormalizedKL structure

Exact equal-parameter normalization in the introduction. The first family is R and the second is P. reflect d p is q^d p(q⁻¹) when p.natDegree ≤ d, which follows here from the degree bound (or the diagonal normalization). The sum is … · OAI.KLInvariance.NormalizedKL

normalizedLaurentCoefficient def

The coefficient chosen in the manuscript, before evaluating at the moving center. · OAI.Nagata.W07.normalizedLaurentCoefficient

normalizedLieParameters def

Parameter data for a fixed normalization by bracket words. · OAI.PolycyclicRecognition.normalizedLieParameters

normalizedLinearMap def

The normalized mass Jacobian, with codomain the zero-sum mass variations. · OAI.Problem358.CellLaplacian.normalizedLinearMap

normalizedMap def

Normalize the given nonvanishing map and retain the closed-ball carrier. · OAI.ThompsonNonamenability.Analytic.normalizedMap

normalizedMassMap def

The actual closed-cell masses, restricted to normalized intercepts. · OAI.Problem358.CellGeometry.normalizedMassMap

normalizedMatrixTrace def

The normalized matrix trace as a positive linear functional. · OAI.KadisonSimilarity.normalizedMatrixTrace

normalizedMatrixTraceLinear def

The normalized sum of the diagonal functionals. · OAI.KadisonSimilarity.normalizedMatrixTraceLinear

NormalizedMidpointWitness structure

A genuine pair law with normalized cell marginals and the geometric midpoint domination. No moment inequality is a field of this witness. · OAI.Problem358.StationaryMoment.NormalizedMidpointWitness

NormalizedMinimalData structure

The normalized reduction data, still in the original ambient norm. The normalization producer uses an actual scalar homothety of the set. · OAI.ReflexiveFixedPoints.NormalizedMinimalData

normalizedModulus def

Exact lower modulus b(r)=1/(8 A^N(r)) from the manuscript. · OAI.AffineBernstein.normalizedModulus

normalizedPacketLattice def

All carrier components share each actual site. The profile bound comes from the single normalized profile, independently of these data. · OAI.LipschitzHilbert.PacketRepresentation.normalizedPacketLattice

NormalizedPair abbrev

Actual normalized pairs, carrying their compact-open topology. · OAI.PolycyclicRecognition.NormalizedPair

normalizedPairMeanSlope def

The averaged slope of the actual evaluation cocycle. · OAI.PolycyclicRecognition.normalizedPairMeanSlope

normalizedPairs def

The first normalized section: the forward map sends the identity to itself. · OAI.PolycyclicRecognition.normalizedPairs

normalizedPairWeight def

Normalize finite two-index masses by their total mass. · OAI.LeanBlast.GotsmanLinial.normalizedPairWeight

normalizedParameterError def

The actual globally centered dictionary score error, divided by its type intensity. The dictionary, sites, and mark alphabets are allowed to vary with N. · OAI.DilutedSpinGlass.PhysicalRoot.normalizedParameterError

normalizedPatchCutoff def

The coordinate cutoff centered at a point of the original metric space. · OAI.RegularPointCoordinates.normalizedPatchCutoff

normalizedPatchDomain def

The original-space active domain for one actual normalized cutoff. · OAI.RegularPointCoordinates.normalizedPatchDomain

NormalizedPencil structure

Positive unital diagonal blocks with an exact Schur-complement equivalence. · OAI.Paper256.NormalizedPencil

normalizedPermutationContraction def

Normalizing each cycle trace by the matrix dimension gives the coordinate formula for the normalized cycle-trace form Φ_π in the paper. · OAI.KadisonSimilarity.normalizedPermutationContraction

normalizedPermutationMultilinear def

The bundled normalized cycle-trace form. · OAI.KadisonSimilarity.normalizedPermutationMultilinear

normalizedPoissonDefect def

The second term is the actual curvature remainder in the shifted Poisson mass estimate, in the same normalized units as the full source. · OAI.RegularPointCoordinates.normalizedPoissonDefect

normalizedPolarTemplates def

Normalized templates ordered as source, reverse anchor, within-tile. · OAI.PolycyclicRecognition.normalizedPolarTemplates

normalizedPolynomial def

The normalized polynomial family appearing in the unshifted weights. · OAI.MatrixMultiplication.AuxiliarySeparation.Sector.normalizedPolynomial

normalizedPrediction def

The normalized step prediction. · OAI.LipschitzHilbert.normalizedPrediction

normalizedPrimeFactor def

The logarithmic size of the largest prime factor of n, measured at base. · OAI.JointDickman.normalizedPrimeFactor

normalizedRectangle def

The normalized rectangle has exactly the same count as the paper's moving-power event. · OAI.JointDickman.normalizedRectangle

normalizedRectangularDerivation def

Rescaling the derivation before forming the triangular representation. · OAI.KadisonSimilarity.normalizedRectangularDerivation

NormalizedResidueData structure

Arithmetic residue information on the canonical geometric levels. The normalized Fourier conclusion, exceptional count, shifted-divisor moment, and terminal shrinking residue remain explicit hypotheses. All geometric alignment, ceiling … · OAI.Problem337.GeometricDensity.NormalizedResidueData

normalizedResidueFamily def

The zero modulus is unused by prime samples. This total definition lets both histories evaluate the same transform at their actual sampled prime. · OAI.Ostmann.normalizedResidueFamily

normalizedResidueMap def

Divide each actual residue coefficient by its nonzero normalization scalar. · OAI.Nagata.Workers.W10.normalizedResidueMap

normalizedResponse def

The response coefficient and columns in the actual homogeneous space. · OAI.MaxCutGames.Decoder.SelectedPolicies.normalizedResponse

normalizedResponse def

The response coefficient and columns in the actual homogeneous space. · OAI.UniqueGamesTheorem.Decoder.SelectedPolicies.normalizedResponse

normalizedRestriction def

Normalize the restriction to a region of positive finite mass. · OAI.PolycyclicRecognition.normalizedRestriction

normalizedRipsFamilyBoundary def

An actual whole-union Roe class for every family of compact-source cycles, with all normalization premises discharged. · OAI.CoarseAssembly.Rips.normalizedRipsFamilyBoundary

normalizedScalarHelmholtz def

The normalization follows the Fourier convention used by Mathlib: J² = 1 - (2π)⁻² Δ. · OAI.PositiveEinsteinFour.Geometry.normalizedScalarHelmholtz

normalizedSchwartzScale def

The normalized dilation w(v/δ)/δ, for a positive window scale. · OAI.JointDickman.normalizedSchwartzScale

NormalizedSimplexIdentities structure

The classical normalized-chain identities. · OAI.Thomason.Construction.NormalizedSimplexIdentities

NormalizedSolution abbrev

The canonical locus is a subtype of the full solution, retaining all old equations, all ordered vertices and all quotient identifications. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.NormalizedSolution

normalizedSourceLower def

Lower threshold after rounding and removing a scalar identity term. · OAI.ContinuumCoulomb.normalizedSourceLower

normalizedSourceThetaSection def

The manuscript's normalized theta section as a genuine holomorphic multiplier section, with the common multiplier gamma=epsilon*tau^sigma. · OAI.Nagata.W09.normalizedSourceThetaSection

normalizedSourceUpper def

Upper threshold after rounding and removing a scalar identity term. · OAI.ContinuumCoulomb.normalizedSourceUpper

normalizedSpace def

The hyperplane of intercepts with weighted average zero. · OAI.Problem358.CellLaplacian.normalizedSpace

normalizedStates def

Additive restriction-monotone states with a fixed detector inequality. · OAI.MatrixMultiplication.AuxiliarySeparation.normalizedStates

normalizedStepBound def

The explicit normalized metric error of a constructed step. Its dependence on the uncontrolled input norm C is linear. · OAI.ClosedSurfaceR4.FiniteOrderSmoothing.MetricGoodPhaseData.normalizedStepBound

normalizedSum def

The normalized sum uses an actual finite product space at every index. · OAI.SquareRootDegree.FiniteCLT.normalizedSum

normalizedThetaDerivativeSeries def

Sum of the explicit derivative summands. Identification with the derivative of normalizedThetaSeries is recorded separately. · OAI.Nagata.W22.normalizedThetaDerivativeSeries

normalizedThetaDerivativeTerm def

The candidate order-c derivative summand, with its explicit frequency factor. · OAI.Nagata.W07.normalizedThetaDerivativeTerm

normalizedThetaSection def

The normalized integer-frequency theta series as a genuine global multiplier section. · OAI.Nagata.W08.normalizedThetaSection

normalizedThetaSeries def

Exactly the bilateral exponential series of equation eq:normalized-theta. · OAI.Nagata.W22.normalizedThetaSeries

normalizedThetaTerm def

The actual normalized Laurent summand in logarithmic local coordinates. · OAI.Nagata.W07.normalizedThetaTerm

normalizedTrace def

Normalize the ambient trace by the trace of the corner identity. · OAI.KadisonSimilarity.CStarCorner.normalizedTrace

normalizedTranslate def

Translate a state by multiplication, then normalize at the unit. · OAI.MatrixMultiplication.AuxiliarySeparation.normalizedTranslate

normalizedTranslate def

Translation as a map of the compact normalized section. · OAI.PolycyclicRecognition.normalizedTranslate

normalizedWeights def

The normalized section of a monomial cone; a i is the positive discrepancy of its primitive ray in the application. · OAI.CartierSections.normalizedWeights

normalizedWeylCoordinates def

For Ricci=3g this is exactly the Weyl four-tensor. Defining its coordinate field first ensures that derivatives are taken before choosing eigenframes. · OAI.PositiveEinsteinFour.Geometry.normalizedWeylCoordinates

normalizeFinite def

Normalization is defined even for the zero measure, using a harmless atom. · OAI.BoltzmannNonuniqueness.SheetMeasures.normalizeFinite

normalizeFrame def

Correct an arbitrary polynomial lift to the prescribed initial frame by a constant, invertible fiber scaling. · OAI.StableCoordinate.FrameLift.normalizeFrame

normalizeFunction def

Radial retraction to the old L1 unit ball, pointwise on representatives. · OAI.ExactModuli.KW.normalizeFunction

normalizeLocalL2 def

Scaling by the norm of the constant function is the normalized local L² convention; the zero-measure case uses the usual inverse-zero convention. · OAI.RegularPointCoordinates.normalizeLocalL2

normalizeNeg def

Negative radial normalization, with the field's usual value at zero. · OAI.ThompsonNonamenability.Analytic.normalizeNeg

normalizePair def

Every pair satisfying the actual coarse bounds has a normalized representative. · OAI.PolycyclicRecognition.normalizePair

normalizePath def

Divide each homogenized path by s's on the target side. · OAI.LittleFinitistic.QuadraticEncoding.normalizePath

normalizePolynomialFrame def

Normalize an ordinary-polynomial frame to a prescribed initial frame. · OAI.StableCoordinate.FrameLift.normalizePolynomialFrame

normalizeQuaternion def

Radial normalization is only used on nonzero quaternions. The harmless value at zero makes it a total function without changing that domain. · OAI.EilenbergGanea.normalizeQuaternion

normalizer def

The positive finite normalizing sum of the optimal Selberg weights. · OAI.Problem337.SelbergOptimal.normalizer

normalizerGroup def

The normalizers of a concrete von Neumann algebra as an actual subgroup. · OAI.KadisonKastler.normalizerGroup

normalizeSimplex def

Remove degeneracies from a simplex and push forward its barycentric coordinates. · OAI.Thomason.Construction.RealizationPrism.normalizeSimplex

normalizeSupported def

First discard zero coordinates, then remove degeneracies from the supported simplex. · OAI.Thomason.Construction.RealizationPrism.normalizeSupported

normalizingBoundaryBases def

The explicit inverse prefix product at every boundary corner. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.normalizingBoundaryBases

NormalizingFamily def

Uniformly bounded families all of whose values normalize the algebra. · OAI.KadisonKastler.NormalizingFamily

normalLineEquiv def

The unit-speed isometry from the real line to the span of a nonzero normal. · OAI.Problem358.TangentNormalCoordinates.normalLineEquiv

normalMap def

Unit-speed normal displacement plus a tangential vector. · OAI.Problem358.TangentNormalCoordinates.normalMap

normalMatrixTower def

The same full-matrix tower in the concrete normal coordinates. · OAI.KadisonSimilarity.TracialCornerGeometry.normalMatrixTower

normalMinusMarkedMultiplier def

The multiplier of A=L^3⊗O(-P), in fixed covering-space frames. · OAI.Nagata.CoefficientSpaces.normalMinusMarkedMultiplier

normalMultiplication def

The normal pairing in a multiplication layer, including equal coordinates. · OAI.Problem335.FactorialExpansion.normalMultiplication

NormalPIn def

A p-subgroup of J normalized by every element of J. · OAI.PCoreCancellation.NormalPIn

normalPlane def

The actual two-dimensional linear plane of a unit normal. · OAI.TriangularCovering.normalPlane

normalProjection def

The complement of the fixed subspace. · OAI.EilenbergGanea.normalProjection

normalRangeSupport def

The range support viewed as an element of its original normal algebra. · OAI.KadisonSimilarity.normalRangeSupport

normalResiduePolynomial def

Polynomial of residue classes along the principal equation G. · OAI.Nagata.Workers.W24.normalResiduePolynomial

normalRestriction def

The normal restriction of a bilinear form written in coordinate components. · OAI.PositiveEinsteinFour.Geometry.normalRestriction

normalSectionAction def

Conjugation on Q / (Q ∩ L) transported through theta. · OAI.FiniteLattice.CommonCore.normalSectionAction

normalSpace def

The actual normal plane of the immersed tangent plane. · OAI.ClosedSurfaceR4.SphericalJets.normalSpace

normalTraceCandidate def

The tracial weight on the GNS weak operator closure. · OAI.TraceConeClassification.ExtendedTrace.normalTraceCandidate

normalUnitaryEquiv def

The same action restricted to normal functionals. · OAI.BoundedHochschild.KadisonRingrose.normalUnitaryEquiv

normalVariation def

The graph's normal component of an arbitrary parametrized velocity. · OAI.AffineBernstein.normalVariation

normalVCorrection def

The V correction before averaging the path labels. · OAI.Problem335.MomentPairing.normalVCorrection

normalVLayers def

Normal pairing layers belonging to the derivative-variable group. · OAI.Problem335.MomentPairing.normalVLayers

normalWedge def

Exterior multiplication by the normal covector, expressed by the standard alternating sum. It is used only to verify the surface density. · OAI.Mahler.normalWedge

normalWordPicture def

A normalized actual cone disk defines a word picture whose every interior face has a proved cost30 replacement. The protected exterior is EXCLUDED. · OAI.HyperbolicObstruction.ConeSkeleton.normalWordPicture

normAmbient def

The same actual values in the original normed space. · OAI.ReflexiveFixedPoints.WeakSelfMap.normAmbient

normCollectedCoeff def

Collection by rational norm, with no change to the coefficients. · OAI.CubicFirstMoment.normCollectedCoeff

normCountingSum def

Cumulative count of an arithmetic sequence collected by integer norm. · OAI.CubicFirstMoment.normCountingSum

normedLieBracket def

Continuous realization of the bracket in the given finite-dimensional norm. · OAI.PolycyclicRecognition.normedLieBracket

NormerStep structure

One finite stage of the normer construction. · OAI.SeparableQuotient.NormerStep

normFiberMultiplicity def

The actual largest multiplicity when distinct Eisenstein integers have the same positive rational norm. · OAI.CubicFirstMoment.normFiberMultiplicity

normFn def

Norm of a bounded vector field, still an arbitrary bounded function on this discrete domain. · OAI.PlaneFiveColor.InvariantMean.normFn

NormGeneratedExtension def

The norm-closed unital star algebra generated by the source and one element. · OAI.KadisonKastler.NormGeneratedExtension

norming def

The full norming set obtained from finite-stage pure and mixed operations. · OAI.SeparableQuotient.ActualSpace.norming

normPrimeInterval def

Independently prescribed interval of primary primes. · OAI.CubicFirstMoment.normPrimeInterval

normSq def

Euclidean squared norm, not the sup norm of the Pi ambient Banach space. · OAI.ArnoldCounterexample.Forms.normSq

normSq def

Squared Euclidean norm in a triangular lattice of unit spacing. · OAI.Problem160.SevenLattice.normSq

normSqCoefficients def

The genuine coefficients of the squared norm on an affine line. · OAI.QuantitativeVanDerWaerden.normSqCoefficients

normSqMap def

Squared modulus of a continuous complex function, kept real-valued. · OAI.KervaireSpectral.normSqMap

normStamp def

Prices in true history. · OAI.FourierLLogL.Dyadic.Procedure.Paths.CastShow.normStamp

normToWeak def

Change only the carrier; both representatives denote the same point. · OAI.ReflexiveFixedPoints.normToWeak

normTwist def

The norm twist at real Mellin height u. · OAI.CubicFirstMoment.normTwist

NormUltrapower abbrev

The exact quotient l-infinity(N,B)/I_omega(B) as a complex star algebra. The quotient identifies sequences whose difference tends to zero along the ultrafilter. · OAI.NuclearUltrapower.NormUltrapower

normUltrapowerMk def

The canonical quotient map, preserving the unit and the complex star algebra. · OAI.NuclearUltrapower.normUltrapowerMk

normUltraToCStar def

Endow the norm-null ring quotient with its canonical C*-model, without replacing the norm-null ideal by any algebraic relation. · OAI.NuclearUltrapower.normUltraToCStar

normUnit def

The unit value is the localized character value, not an unrelated witness. · OAI.CirculantHadamard.BinaryLocalRing.normUnit

normW def

Divide a finite weight function by its total, giving zero if total is zero. · OAI.HadwigerCounterexample.normW

normWeight def

The rational weight R_v in equation (15). · OAI.PositiveEinsteinFour.normWeight

normWeightedSum def

Its power-weighted cumulative sum. · OAI.CubicFirstMoment.normWeightedSum

NoSparse def

There is no active internal node with fewer than b active children. · OAI.TreeEdit.BinaryLower.TreeDistortion.FiniteMass.NoSparse

NoTripleTies def

No three distinct affine scores agree at the point. · OAI.Problem358.TripleTieAvoidance.NoTripleTies

NoTypeII1Summand def

There is no nonzero finite central corner with no type I central part. · OAI.BoundedHochschild.KadisonRingrose.NoTypeII1Summand

NPVerifier structure

Polynomially bounded certificates checked by an actual deterministic finite-alphabet machine, on the explicitly encoded input/certificate pair. · OAI.DirectedFeedback.NPVerifier

NPVerifier structure

A standard polynomial-time Boolean verifier. FinTM2 already requires finitely many stacks, control labels, and internal states; this field also requires every stack alphabet to be finite. The actual machine runs on the explicit paired … · OAI.MaxCutGames.Foundations.Complexity.CookLevin.NPVerifier

NPVerifier structure

A standard polynomial-time Boolean verifier. FinTM2 already requires finitely many stacks, control labels, and internal states; this field also requires every stack alphabet to be finite. The actual machine runs on the explicit paired … · OAI.UniqueGamesTheorem.Foundations.Complexity.CookLevin.NPVerifier

nu def

The conditional old-location law of the single designated optimum mover. · OAI.KServer.FiniteExperiment.nu

nuclear_quotient_modular_corner_represented_bound abbrev

The concrete bound is the direct specialization of the represented finite-tracial bound, with its canonical GNS structures kept intact. · OAI.WeakPureInfiniteness.nuclear_quotient_modular_corner_represented_bound

NuclearCPAP def

The completely positive approximation property, in norm finite-test form. · OAI.TraceConeClassification.NuclearCPAP

NuclearData structure

Finite clamped-nucleus data for binary-encoded positive integer charges. · OAI.ContinuumCoulomb.NuclearData

nullHomotopy def

The sign-correct null-homotopy required by RectificationTotal.total. · OAI.ExternalTensor.Section4.nullHomotopy

nullHomotopy def

Zero in K means a genuine right-linear null-homotopy of the chain representative. · OAI.LittleFinitistic.BoundedHomotopy.nullHomotopy

nullSubgroup def

Freely represented words admitting a finite disk construction. · OAI.HyperbolicObstruction.WordPictures.nullSubgroup

nullSubgroup def

Words reducible to the empty word form a subgroup of the free group. · OAI.KaplanskyCounterexample.WordReduction.nullSubgroup

number def

The index equivalence is routine, but we record it to compile a nonempty-state table to the concrete Machine class. · OAI.ExactDerandomization.Table.TM.number

number def

Little-endian packing, used solely for proving exhaustive mask coverage. · OAI.WLIdentification.NumericGraph.number

NumberIndex abbrev

The number-basis indices for n bosonic modes. · OAI.EntropyPhotonNumber.NumberIndex

numberKet def

A number-basis vector. · OAI.EntropyPhotonNumber.numberKet

numeratorIdeal def

Numerators whose division by T lies in a specified Laurent subalgebra. · OAI.StableCoordinate.ModificationPieces.numeratorIdeal

numeratorLine def

The numerator v * Hminus - w * Hplus, with the ancestor denominator still cleared. The current compensation variable does not occur here. · OAI.Ostmann.PolynomialGiantRows.numeratorLine

NumericalWitnessEvent def

All conditions involve the original numerical main and witness words. · OAI.TwoPointCorrelations.NumericalWitnessEvent

numericEdgeEquiv def

The occurrence e occupies output indices 4e,4e+1,4e+2,4e+3. · OAI.MaxCutGames.Explicit.SubdivisionTarget.numericEdgeEquiv

numericEdgeEquiv def

The occurrence e occupies output indices 4e,4e+1,4e+2,4e+3. · OAI.UniqueGamesTheorem.Explicit.SubdivisionTarget.numericEdgeEquiv

numericRightEquiv def

Number p_e by 2e and r_e by 2e+1. · OAI.MaxCutGames.Explicit.SubdivisionTarget.numericRightEquiv

numericRightEquiv def

Number p_e by 2e and r_e by 2e+1. · OAI.UniqueGamesTheorem.Explicit.SubdivisionTarget.numericRightEquiv

numericVector def

The actual 3237 coordinates used by the mixed numerical certificate. · OAI.MUB6.Certificate.MixedSemantics.numericVector

numericVertexEquiv def

Original vertices, middle vertices, then interleaved p_e,r_e. · OAI.MaxCutGames.Explicit.SubdivisionTarget.numericVertexEquiv

numericVertexEquiv def

Original vertices, middle vertices, then interleaved p_e,r_e. · OAI.UniqueGamesTheorem.Explicit.SubdivisionTarget.numericVertexEquiv