Glossary: V

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

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V abbrev
The source's completed polynomial blowup V, as literal base change. · OAI.KummerSourceModel.V
v def
The global generator of the pulled-back ideal. · OAI.StableCoordinate.Bundle.v
v def
The distinguished element of source equation bun:v. · OAI.StableCoordinate.DeterminantRing.v
v0 def
The specified first point and first matrix coordinate in their inherited orders. · OAI.KaplanskyCounterexample.Prescription.Output.v0
V0Iso def
Evaluation of the one fixed actual V0 is precisely eY direct-sum eY[3]. · OAI.LittleFinitistic.SelectedDiagramEvaluation.V0Iso
v2Inclusion def
F>=2 really is V2, embedded by its original vertex summand inclusion. · OAI.ExternalTensor.Section4.SourceFiltration.v2Inclusion
vacuum abbrev
The actual exceptional subspace consists of words whose initial D coordinate is the scalar trace vector. · OAI.KadisonSimilarity.TracialHeadCoordinates.vacuum
vacuumColumn def
A literal column with unmarked top and bottom ports. · OAI.CriticalHoneycomb.Transfer.PlanarNormalization.vacuumColumn
vacuumSubspace def
The actual vacuum subspace in a completed head-tail tensor product. · OAI.KadisonSimilarity.vacuumSubspace
valence def
Number of flags, including legs, incident to a vertex. · OAI.PixtonChow.StableGraph.valence
Valid def
An input is `Valid` when it has at least one vertex, has positive `k`, and its explicit or expanded multigraph is $k$-edge-connected. · OAI.AlgorithmicThinTrees.Valid
Valid def
Every same edge strictly decreases physical depth and never increases rank. Every earlier edge strictly decreases rank and never increases depth. No global count is part of this certificate. · OAI.EditApproximation.DependencyExpansion.Valid
Valid inductive
Complete-data acceptance. The local tests are finite prime checks and a product check, followed by EXACT ordered children; no witness fields or advice. · OAI.ExactQuantumFactoring.FactorData.Valid
Valid structure
Finite-length invariants for the simultaneous noncommutative-root induction. The distant invariant bounds the maximum, not the sum, of the two word lengths. · OAI.FiniteAlgebraicEnvelopes.SteinbergFiniteFree.SmallSystem.Valid
Valid def
Exactly compact metric probability spaces, with their Borel sigma algebras. · OAI.FKCRT.MetricMeasureData.Valid
Valid def
valid with active prefix · OAI.FourierLLogL.Dyadic.Procedure.Wire.Valid
Valid def
Actual validity tests reject local overlap. Top and background disjointness are automatic from the layout, and are stated here to expose the invariant. · OAI.LowSpaceSubsetSum.RepresentationUniverse.Valid
Valid def
The two graph laws are decidable finite checks on the stored rows. · OAI.MaxCutGames.Foundations.PCP.GenericGraphTables.Valid
Valid def
The two graph laws are decidable finite checks on the stored rows. · OAI.MaxCutGames.Foundations.PCP.GraphTables.Valid
Valid def
The indicated pair identifications must already be an equivalence, without adding further overlaps by transitive closure. Equality within a copy is built into Rel. · OAI.PartitionConsistency.DiagramForcing.OverlapPrescription.Valid
Valid structure
All data needed to extend a body, except the body entries themselves. · OAI.Problem348.GuardedPath.AnchorFrame.Valid
Valid structure
Explicit original-matrix conditions on a selected path. The frame validity contains all required order comparisons and all 64-anchor signatures. · OAI.Problem348.GuardedPath.Selection.Valid
Valid def
Every predicate is a countable combination of Borel coordinate predicates. Midpoint membership entails the entire open-flight condition by convexity. · OAI.TriangularBilliards.ChainData.Valid
Valid def
Exact interpretation of the source constraints, over either rationals or reals. · OAI.UniformKServer.EffectiveLP.Valid
Valid def
A raw nonendpoint portion has at most k distinct requested points. Marks are a subset of the points already seen in that same raw block. · OAI.UniformKServer.Fallback.Valid
Valid def
Exact interpretation of the source constraints, over either rationals or reals. · OAI.UniformKServer.OffsetLP.Valid
Valid def
The two graph laws are decidable finite checks on the stored rows. · OAI.UniqueGamesTheorem.Foundations.PCP.GenericGraphTables.Valid
Valid def
The two graph laws are decidable finite checks on the stored rows. · OAI.UniqueGamesTheorem.Foundations.PCP.GraphTables.Valid
valid def
Prefixes whose remaining section meets the interior of the body. · OAI.Problem358.ConvexTriangularSampler.valid
valid def
Only odd-role child terms may acquire an active parent multiplier. · OAI.TraceReconstruction.OccupiedParityTree.valid
ValidCandidate def
The literal modular-power verification in all three trial modes. · OAI.ExactQuantumFactoring.OrderTrial.ValidCandidate
ValidCycleSlots def
A permutation-cycle collection in distinguishable slots, including all length-one cycles. No selection has been weakened to a collection of paths. · OAI.CubeShuffle.RoutingNetwork.ValidCycleSlots
ValidCycleSlots def
A permutation-cycle collection in distinguishable slots, including all length-one cycles. No selection has been weakened to a collection of paths. · OAI.CubeShuffle.ValidCycleSlots
ValidInput def
An injection into the actual available input slots. · OAI.CoordinateSweeps.Grid.Holes.ValidInput
validJ def
Satisfaction and consistency over all 3*u occurrence slots. · OAI.MaxCutGames.Foundations.Hastad.SourceContexts.validJ
validJ def
Satisfaction and consistency over all 3*u occurrence slots. · OAI.UniqueGamesTheorem.Foundations.Hastad.SourceContexts.validJ
ValidTransferNode structure
The conditions used by the rigidity argument are all original support conditions or the strict product-range inequality. · OAI.Ostmann.ValidTransferNode
ValidWindowEdge def
An edge is identified with the nonempty path to its child. · OAI.Problem310.ValidWindowEdge
valuation def
Genuine monomial valuation on the formal regular local ring, including faces with zero weights. · OAI.CartierSections.FormalMonomial.valuation
valuation def
Weighted monomial valuation on the genuine polynomial coordinate ring. · OAI.CartierSections.Monomial.valuation
valuationConstraints def
Literal evaluation constraints from the common lc slice, on the ambient space of readings of regular functions. In use m j is the positive integer multiplicity from E, and the normalization of discrepancy is imposed by the normalized … · OAI.CartierSections.valuationConstraints
valuationTail def
Upper tail of a natural-number-valued random variable, written for a nonnegative discrete mass function. · OAI.DukePrimeDegree.valuationTail
Value def
Values of the spatial derivative of order n. The type synonym fixes one normed-space structure throughout the jet family. · OAI.ForcedComputation.BoundedSpatialJets.Value
value def
Literal coefficient-weight infimum of a formal power series. · OAI.CartierSections.FormalMonomial.value
value def
The value is the minimum monomial weight, with value infinity at zero. · OAI.CartierSections.Monomial.value
value def
Last raw bit index is width-1; extra coordinate index width. · OAI.Fifths.Circuit.value
value def
The orbit-indexed difference; the selected representative is immaterial. · OAI.FiniteAlgebraicEnvelopes.StabilizerCocycle.value
value def
The value forced by the native derivation on a finite simple subextension. · OAI.GrahamSpherical.AlgebraicExtension.value
value def
The collar and cap formulas retain each occurrence's independent cornerOffset. · OAI.HyperbolicObstruction.FinitePolygonModel.Data.value
value def
Chosen only from genuine, exactly marked genus-zero disks. · OAI.HyperbolicObstruction.IndexedFilling.value
value def
A maximum of the finitely many actual deterministic success probabilities. · OAI.MaxCutGames.Foundations.Games.Game.value
value def
The usual instance value: the largest satisfied fraction of its stored constraint list. The denominator is positive by the Instance invariant. · OAI.MaxCutGames.Integration.InstanceValue.value
value def
The value of a canonical basis in a pair of cell tables. · OAI.Thomason.Construction.PastingGlobeBasis.value
value def
Value assigned by a compatible cocone to a bounded cell. · OAI.Thomason.Construction.StrictOmegaCategory.GlobePasting.value
value def
A maximum of the finitely many actual deterministic success probabilities. · OAI.UniqueGamesTheorem.Foundations.Games.Game.value
value def
The usual instance value: the largest satisfied fraction of its stored constraint list. The denominator is positive by the Instance invariant. · OAI.UniqueGamesTheorem.Integration.InstanceValue.value
valueMap def
A zero-order multilinear value is an ordinary value. · OAI.ForcedComputation.BoundedSpatialJets.valueMap
valueOnTensorClass def
A character has a well-defined value on mutual-restriction classes. · OAI.MatrixMultiplication.AuxiliarySeparation.Character.valueOnTensorClass
Values structure
Numeric interpretations are proof-side data, separate from the program. · OAI.MaxCutGames.Reduction.MachineOutcomeRows.Values
Values structure
Numeric interpretations are proof-side data, separate from the program. · OAI.UniqueGamesTheorem.Reduction.MachineOutcomeRows.Values
values abbrev
Alias for the canonical source-ordered Laurent coordinate values. · OAI.StableCoordinate.ModificationEmbedding.values
vanishingFiltration def
The exact vanishing filtration, expressed by low Taylor coefficients. · OAI.RationalHitting.Expansion.vanishingFiltration
Var abbrev
Actual amalgamated fields: one copy in U, one copy per branch outside U. · OAI.HyperbolicObstruction.StarModel.Var
var2 def
Variance around the finite average. · OAI.ExactDerandomization.Analysis.var2
variableElement def
A variable as a member of its assigned image-filtration piece. · OAI.StableCoordinate.GradedPresentationMap.variableElement
VariableInput structure
The variable player's input contains full occurrences or variable names, with no occurrence attached to a singleton name. · OAI.UniqueGamesTheorem.Clean.LocalReplay.VariableInput
variableOperator def
The endomorphism assigned to an individual variable. · OAI.Problem335.variableOperator
Variables structure
A chart's actual label variables, not hypothetical independent coordinates. The preservation proof is exactly the joint Lebesgue/fair-sign invariant. · OAI.PlanarL1.Threshold.Variables
Variables abbrev
Complexified variables; the extra variable forces a square root of -1 into the field, so every archimedean place is complex. · OAI.WeakPinned.Transfer.Variables
variableSlots def
Each coordinate selects its own loaded variable field, even if names repeat. · OAI.MaxCutGames.Foundations.Hastad.SourceRankPhase.variableSlots
variableSlots def
Each coordinate selects its own loaded variable field, even if names repeat. · OAI.UniqueGamesTheorem.Foundations.Hastad.SourceRankPhase.variableSlots
variableSupportLabels def
The three class labels that can contain ones in a variable row. · OAI.Problem348.Construction.variableSupportLabels
variance def
The mean-subtracted variance in the probability normalization. · OAI.PettyProjection.Spherical.variance
Variant def
each fixed guessed variant permutes the full environment and does not involve its not-yet-known retained point y. · OAI.ExactDerandomization.Analysis.Wrap.Variant
variationalFunctional def
Equation (1.8), with the infimum outside the field supremum. · OAI.InvariantIsing.variationalFunctional
variationBudget def
The whole-table TV budget includes the coefficient of both compared events in the witness-margin inequality. · OAI.MaxCutGames.Decoder.ConstantSelection.variationBudget
variationBudget def
The whole-table TV budget includes the coefficient of both compared events in the witness-margin inequality. · OAI.UniqueGamesTheorem.Decoder.ConstantSelection.variationBudget
variationConormal def
The conormal for the genuine variation (x+t a(x),u(x)+t beta(x)), written in its first jets, is (-q(t),1). · OAI.AffineBernstein.variationConormal
variationCube def
Cubed variation of a finite scalar sequence. Repetitions in the monotone list allow every shorter partition to be padded to length N + 1. · OAI.LipschitzHilbert.variationCube
variationFromUniform def
Total variation with the manuscript's convention ½ ∑ |p-u|. · OAI.ContingencyTables.FairBits.variationFromUniform
variationSecondForm def
The second form for that conormal. H,B are the Hessians of u,beta; C k is the Hessian of the kth horizontal displacement. · OAI.AffineBernstein.variationSecondForm
varyingRowBase def
Lookup scan suffixes and other work tapes may evolve between vertices. Only the output field is replaced by the prescribed canonical row suffix. · OAI.MaxCutGames.Foundations.Complexity.PoweringMachineLoop.varyingRowBase
varyingRowBase def
Lookup scan suffixes and other work tapes may evolve between vertices. Only the output field is replaced by the prescribed canonical row suffix. · OAI.UniqueGamesTheorem.Foundations.Complexity.PoweringMachineLoop.varyingRowBase
varyingSequenceEval def
Evaluation in the j-th finite factor. · OAI.KadisonKastler.varyingSequenceEval
varyingSequenceHom def
A uniformly contractive family of star homomorphisms defines a homomorphism into the bounded varying product. · OAI.KadisonKastler.varyingSequenceHom
varyingSequenceMap def
Coordinate star embeddings into a fixed factor induce the map on bounded products used for the finite-matrix model. · OAI.KadisonKastler.varyingSequenceMap
VaryingTraceQuotient structure
The quotient and its canonical trace formula for a varying product. · OAI.KadisonKastler.VaryingTraceQuotient
varyingUnitarySequence def
A family of coordinate unitaries is bounded in the actual product. · OAI.KadisonKastler.varyingUnitarySequence
Vase structure
A visit whose (single) optional subterminal path is delegated. The hop tokens forward/back are determined by the selector's code, which belongs to a short range. Its pure action compiled at leaves can incorporate post label maps. · OAI.ExactDerandomization.Glass.Vase
Vec abbrev
Vec is allowed to have "ghost" coordinates above the finite width. Every packed access uses just first d+1 coordinates. Gives less cast-burdened proofs about loops. The actual registers store only the charged coordinates. · OAI.Fifths.Modulus.Vec
Vector abbrev
`Vector n` abbreviates the function type `Fin n → F2`, so a vector is one modulo-two coordinate for each of `n` positions. · OAI.UniqueGamesTheorem.Integration.BinaryLinear.Vector
vector def
Assemble an arbitrary vector of single-bit combinational outputs, retaining separate traces. This is a finite circuit construction, not a truth table. · OAI.ExactQuantumFactoring.BooleanNetwork.vector
vector def
Points A,B,C,D followed by the three remaining nonzero vectors. · OAI.HyperbolicObstruction.IncidenceTemplate.vector
vector def
The quotient vectors first, followed by the determinant-kernel vectors. · OAI.MatrixMultiplication.AuxiliarySeparation.DeterminantBasis.vector
vector def
The ordered quotient/kernel vectors in the actual polynomial pair space. · OAI.MatrixMultiplication.AuxiliarySeparation.DeterminantFiltration.vector
vector def
Active points get a single component coordinate; inactive points get zero. The finite coordinate set consists of all subsets of columns. · OAI.PlanarL1.Columns.Model.Activity.vector
vector def
The actual chain vector associated to each formal tensor basis. · OAI.Thomason.Construction.PastingGlobeCylinderBasis.vector
vectorAmplitude def
The amplitude at a question is the sum of its original label entries. · OAI.MaxCutGames.Repetition.ProjectionKernel.vectorAmplitude
vectorAmplitude def
The amplitude at a question is the sum of its original label entries. · OAI.UniqueGamesTheorem.Repetition.ProjectionKernel.vectorAmplitude
vectorCLM def
The continuous vector functional on all bounded operators. · OAI.KervaireSpectral.vectorCLM
vectorData def
The dense-coordinate presentations of the three distinct recursive Banach spaces. Each space is the completion for its displayed, exact finite norm. · OAI.DiamondDistortion.RecursiveModel.vectorData
vectorDotListWithWork def
Dot product over an explicit list of array indices. · OAI.EditApproximation.vectorDotListWithWork
vectorFactorsEquivMatrixVertexChartNeighbors def
Uniform independent nonzero vector factors induce exactly uniform neighbors of the actual Grassmann vertex within the matrix chart. · OAI.MaxCutGames.Inverse.MatrixChart.vectorFactorsEquivMatrixVertexChartNeighbors
vectorFactorsEquivMatrixVertexChartNeighbors def
Uniform independent nonzero vector factors induce exactly uniform neighbors of the actual Grassmann vertex within the matrix chart. · OAI.UniqueGamesTheorem.Inverse.MatrixChart.vectorFactorsEquivMatrixVertexChartNeighbors
vectorFunctional def
The actual bounded complex-linear vector functional on the original algebra. · OAI.Generator.Tracial.vectorFunctional
vectorFunctional def
A vector functional restricted to the continuous calculus of a normal operator. · OAI.KervaireSpectral.vectorFunctional
vectorLpRepresentation def
Bounded continuous scalar multipliers on vector-valued L². · OAI.WeakPureInfiniteness.vectorLpRepresentation
vectorMass def
The vector mass of the actual density, not an abstract additive tree. · OAI.DyadicHats.vectorMass
vectorMass def
The vector mass of the actual density, not an abstract additive tree. · OAI.SignedDisk.DyadicHats.vectorMass
vectorMeanCorrection def
The finite-dimensional correction obtained by applying the mean to each coordinate. · OAI.PolycyclicRecognition.vectorMeanCorrection
vectorMeasure def
The finite scalar spectral measure of a vector, on the actual spectrum. · OAI.KervaireSpectral.vectorMeasure
vectorNorm def
Exactly the outer Hilbert sum of the root-sum ν_h norms with p_h=1+1/h. · OAI.DiamondDistortion.RecursiveModel.vectorNorm
vectorOrder def
Lexicographic order on coefficient/coordinate vectors, increasing index first. · OAI.KaplanskyCounterexample.Prescription.vectorOrder
vectorPositiveFunctional def
A vector state before normalizing its vector. · OAI.BoundedHochschild.KadisonRingrose.vectorPositiveFunctional
VectorQuadraticFormsAgree def
Equality of the quadratic forms represented by one vector and by a finite family of vectors, tested on an operator star subalgebra. · OAI.KadisonSimilarity.VectorQuadraticFormsAgree
VectorStateKMS def
The scalar strip condition at inverse temperature minus one, with the sign convention σ_t(x) = U_t x U_t*. · OAI.KadisonKastler.VectorStateKMS
vectorSum def
The linear sum of the coordinates weighted by v. · OAI.ContingencyTables.vectorSum
vectorSum def
The unnormalized finite sum of vector functionals used for matrix traces. · OAI.KervaireSpectral.vectorSum
vectorValue def
The original Hilbert-space vector functional on actual projections. · OAI.Generator.Tracial.AlgebraProjection.vectorValue
velocity def
The implicit velocity selected by the inverse of the residual. Its defining equation and uniqueness are proved below under the physical parameter restrictions. · OAI.BoltzmannNonuniqueness.AxialFlow.velocity
Verified structure
The conclusions of the paper's rectification lemma for the explicitly constructed bimodule complex and original vertex insertion maps. · OAI.LittleFinitistic.RectificationLemma.Verified
Vertex def
At every replacement every parent edge receives countably many distinct new vertices. · OAI.DiamondDistortion.Diamond.Vertex
Vertex structure
A disjoint forest: one copy of Nat^{≤h} for every h≥1. · OAI.ForestSpace.Vertex
Vertex abbrev
The literal 15-vertex macro graph: point and line vertices, and the single subdivision vertex of the exceptional incidence D--CD. · OAI.HyperbolicObstruction.MacroGraph.Vertex
Vertex abbrev
The tree of finite sequences of positive integers. · OAI.IndependentProducts.Vertex
Vertex inductive
The ten permitted vertices for the band reduction, complementary-swap replacement. U,Q follow old positive time; A,B follow the opposite orientation. · OAI.IntegralCharacterVarieties.OccurrenceIncidence.ComplementaryPatch.Vertex
Vertex abbrev
One realized key orbit, with no prover-side copy. · OAI.MaxCutGames.Decoder.TableKeysGame.Vertex
Vertex def
Actual ell-dimensional subspaces of the ambient binary vector space. · OAI.MaxCutGames.Inverse.KMS.Vertex
Vertex def
Only realized bodies are vertices; no extra formal records are added. · OAI.MaxCutGames.Reduction.ActualOrbit.Vertex
Vertex structure
The source vertex system includes its root equation. Thus its bounded ideal is tied to this actual diagram, not an independently selected poset. · OAI.PartitionConsistency.LocalDiagramSystem.Vertex
Vertex abbrev
Labels allowed by both adjacent layers. · OAI.Problem335.Pairings.Vertex
Vertex abbrev
The integer coordinates in the triangular-lattice basis e₁ = (1,0), e₂ = (1/2, sqrt(3)/2). · OAI.TriangularSurface.Lattice.Vertex
Vertex abbrev
One realized key orbit, with no prover-side copy. · OAI.UniqueGamesTheorem.Decoder.TableKeysGame.Vertex
Vertex def
Actual ell-dimensional subspaces of the ambient binary vector space. · OAI.UniqueGamesTheorem.Inverse.KMS.Vertex
Vertex def
Only realized bodies are vertices; no extra formal records are added. · OAI.UniqueGamesTheorem.Reduction.ActualOrbit.Vertex
vertex def
Vertex restriction retains the original elements, rather than chosen coordinates. · OAI.ExternalTensor.Section4.ArrowVertex.vertex
vertex abbrev
The actual left vertex functor from B-modules to k-vector spaces. · OAI.LittleFinitistic.LeftVertexHomology.vertex
vertex abbrev
The manuscript's specified vertex idempotent. · OAI.LittleFinitistic.SourceVerdier.vertex
vertex def
The three vertex idempotents, in the manuscript's order. · OAI.LittleFinitistic.ThreeVertexAlgebra.vertex
vertex def
Twice the barycenter of the kth cubical face in a maximal flag. · OAI.SharpLiebThirring.CubeFlags.Flag.vertex
vertex def
The cone vertex belongs to every nonempty-dimensional horn. · OAI.Thomason.Construction.HornContraction.vertex
vertex def
Read a face's last vertex inside the greatest face of a flag. · OAI.Thomason.Construction.NonsingularLastVertex.vertex
vertex def
The strict zero-cell at a vertex, as a full positive globular table. · OAI.Thomason.Construction.SimplexComplex.vertex
vertex def
The actual initial vertex belongs to the first active stage. · OAI.TorsionFreeZeroDivisors.ActiveRoot.vertex
vertex def
Only the first stage fixes the marked initial vertex. · OAI.TorsionFreeZeroDivisors.StageRoot.vertex
vertexAddress def
Both bipartite sides remain distinct address blocks. · OAI.MaxCutGames.Reduction.AddressGame.vertexAddress
vertexAddress def
Both bipartite sides remain distinct address blocks. · OAI.UniqueGamesTheorem.Reduction.AddressGame.vertexAddress
vertexAmount def
The actual vertex amount from §11. · OAI.LipschitzHilbert.vertexAmount
VertexAssembly structure
A finite incidence diagram is specified by a bijection from local ports to global side-germ occurrences. · OAI.IntegralCharacterVarieties.OccurrenceIncidence.VertexAssembly
vertexAssembly def
The original corner construction can now be used WITHOUT accidentally scattering a seam's children between unrelated endpoints. · OAI.IntegralCharacterVarieties.OccurrenceIncidence.PortAssembly.vertexAssembly
vertexBasis def
Every Grassmann vertex admits an ordered basis of the prescribed domain. · OAI.MaxCutGames.Inverse.KMSBasisComparison.vertexBasis
vertexBasis def
The zero-simplex at a specified vertex. · OAI.Thomason.Construction.SimplexComplex.vertexBasis
vertexBasis def
Every Grassmann vertex admits an ordered basis of the prescribed domain. · OAI.UniqueGamesTheorem.Inverse.KMSBasisComparison.vertexBasis
VertexBodyTraces def
A per-vertex body certificate must actually execute in the combined program, preserve the remaining unary vertex counter and caller frame, and prepend precisely that vertex's ordered block of rows. · OAI.MaxCutGames.Foundations.Complexity.PoweringMachineLoop.VertexBodyTraces
VertexBodyTraces def
A per-vertex body certificate must actually execute in the combined program, preserve the remaining unary vertex counter and caller frame, and prepend precisely that vertex's ordered block of rows. · OAI.UniqueGamesTheorem.Foundations.Complexity.PoweringMachineLoop.VertexBodyTraces
vertexChangeSq def
Actual change in the conditional tree mean when one assigned vertex moves by one grid step. All remaining topology coordinates are unchanged. · OAI.DilutedSpinGlass.ReducedTopology.vertexChangeSq
vertexCocone def
The compatible vertex readings form a cocone of sets. · OAI.Thomason.Construction.NormalizedSimplexIdentities.vertexCocone
vertexComparison def
Comparison at this vertex, with the occurrence transports already expressed in the shared facet frames. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.vertexComparison
vertexComponents def
Simplicial edge components map to actual path components. · OAI.Thomason.Construction.RealizationPrism.vertexComponents
vertexCoordinates def
The barycentric mass at each vertex, with repeated vertices combined. The target has finite support even when K has infinitely many vertices. · OAI.Thomason.Construction.RealizationPrism.vertexCoordinates
vertexCost def
Source internal-turn product, retaining a finite, explicit matching error denominator instead of hiding it in o(L). · OAI.TorsionFreeZeroDivisors.StageRealization.vertexCost
vertexCutoffFactor def
An explicit vertex cutoff, zero up to radius R and one outside radius 2R. Its transition annuli are those used in the localized energy bound. · OAI.TriangularBilliards.vertexCutoffFactor
vertexDepth def
Depth and arity refer to the genuine internal vertices, not their sampled values. · OAI.DilutedSpinGlass.PrescribedTree.vertexDepth
vertexEquiv def
Arrange the old vertices, their inserted corners, and the new apices. · OAI.HyperbolicObstruction.PictureSwitch.ConeExpansion.vertexEquiv
vertexEquiv def
Actual A-linear identification of the compressed vertex with its original term. · OAI.LittleFinitistic.OrdinarySimulation.Compression.vertexEquiv
vertexEquiv def
Old vertices occupy the initial interval and dummy vertices the final one. · OAI.MaxCutGames.Foundations.PCP.PreprocessingPaddingTables.vertexEquiv
vertexEquiv def
Row-major indexing before the explicit finite-field blowup. · OAI.OptimalMaxCut.LongCode.InstanceAdapter.vertexEquiv
vertexEquiv def
Explicit lexicographic indexing of all Np^6 output vertices. · OAI.OptimalMaxCut.Unweighted.vertexEquiv
vertexEquiv def
Old vertices occupy the initial interval and dummy vertices the final one. · OAI.UniqueGamesTheorem.Foundations.PCP.PreprocessingPaddingTables.vertexEquiv
vertexEvaluation def
On distinct vertex orbits, equivariant vertex values may be varied independently. · OAI.SharpLiebThirring.PLParity.vertexEvaluation
vertexFiber abbrev
The exact fiber at a vertex of the source's contraction graph. · OAI.PartitionConsistency.LocalDiagramSystem.System.vertexFiber
vertexFields def
The five physical fields consumed by the checked row-emission phase. · OAI.MaxCutGames.Explicit.SubdivisionTarget.vertexFields
vertexFields def
The five physical fields consumed by the checked row-emission phase. · OAI.UniqueGamesTheorem.Explicit.SubdivisionTarget.vertexFields
vertexFixedEquiv def
Identify the actual fixed-point vertex part of M(Y) with Y. · OAI.LittleFinitistic.QuadraticEncoding.Representation.vertexFixedEquiv
vertexFullSubcategory def
The full strict subcategory on the specified oriental vertices. · OAI.Thomason.Construction.SimplexComplex.vertexFullSubcategory
vertexGuardCore def
The unary guard specialized to the concrete extra tape. The zero delimiter is retained; both branches clear the bit register. Its dependent alphabet is the same alphabet used by the embedded row program. · OAI.MaxCutGames.Foundations.Complexity.MachineExpanderTable.vertexGuardCore
vertexGuardCore def
The unary guard specialized to the concrete extra tape. The zero delimiter is retained; both branches clear the bit register. Its dependent alphabet is the same alphabet used by the embedded row program. · OAI.UniqueGamesTheorem.Foundations.Complexity.MachineExpanderTable.vertexGuardCore
VertexHolds def
All permitted vertex conditions on the matrix system. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.VertexHolds
vertexHomMap def
Transport module maps to the concrete degree-zero objects of K. · OAI.LittleFinitistic.QuadraticEncoding.vertexHomMap
vertexIndex def
Vertex classifier for the doubled boundary: vertices are NOT assumed as incidence fields; they are computed from face-turn times side-pairing. · OAI.HyperbolicObstruction.PictureSwitch.PolygonSphere.vertexIndex
vertexIndex def
Explicit mixed-radix vertex coordinates for one square/zigzag step. · OAI.MaxCutGames.Foundations.PCP.ExpanderTables.vertexIndex
vertexIndex abbrev
The chosen greatest vertex, as an actual zero-simplex. · OAI.Thomason.Construction.ConePrism.vertexIndex
vertexIndex def
Explicit mixed-radix vertex coordinates for one square/zigzag step. · OAI.UniqueGamesTheorem.Foundations.PCP.ExpanderTables.vertexIndex
vertexInTime def
Timed execution for the concrete fixed-degree old-row loop. The natural bound is polynomial in vertex count, dart count, and accumulated output size. · OAI.MaxCutGames.Foundations.Complexity.MachineLazyRows.vertexInTime
vertexInTime def
Timed execution for the concrete fixed-degree old-row loop. The natural bound is polynomial in vertex count, dart count, and accumulated output size. · OAI.UniqueGamesTheorem.Foundations.Complexity.MachineLazyRows.vertexInTime
vertexIso def
The exact natural vertex identification E_i tensor_B M(Y) = Y. · OAI.LittleFinitistic.ConcreteTensorEvaluation.vertexIso
vertexIso def
The two concrete presentations of the same right ideal e_i B. · OAI.LittleFinitistic.SourceQuotientAction.vertexIso
VertexIsolated def
Precisely the vertex-isolation condition in the source's definition of good. · OAI.CoordinateSweeps.Grid.Holes.VertexIsolated
vertexK def
The actual degree-zero right vertex projective in K. · OAI.LittleFinitistic.QuadraticEncoding.vertexK
vertexLoopInTime def
Execute every remaining vertex in the common finite table program. · OAI.MaxCutGames.Foundations.Complexity.MachineExpanderTable.vertexLoopInTime
vertexLoopInTime def
Derives the complete outer enumeration trace from the actual row-body traces. Descending cursor order and prepending produce canonical ascending vertex order on the output tape. The zero delimiter is retained for cleanup. · OAI.MaxCutGames.Foundations.Complexity.PoweringMachineLoop.vertexLoopInTime
vertexLoopInTime def
Execute every remaining vertex in the common finite table program. · OAI.UniqueGamesTheorem.Foundations.Complexity.MachineExpanderTable.vertexLoopInTime
vertexLoopInTime def
Derives the complete outer enumeration trace from the actual row-body traces. Descending cursor order and prepending produce canonical ascending vertex order on the output tape. The zero delimiter is retained for cleanup. · OAI.UniqueGamesTheorem.Foundations.Complexity.PoweringMachineLoop.vertexLoopInTime
vertexLoopInTime_varying def
The outer loop with a varying work-tape frame. Actual row-body traces determine that frame; no cleanup of accumulated lookup suffixes is assumed. · OAI.MaxCutGames.Foundations.Complexity.PoweringMachineLoop.vertexLoopInTime_varying
vertexLoopInTime_varying def
The outer loop with a varying work-tape frame. Actual row-body traces determine that frame; no cleanup of accumulated lookup suffixes is assumed. · OAI.UniqueGamesTheorem.Foundations.Complexity.PoweringMachineLoop.vertexLoopInTime_varying
vertexMap def
The greatest vertex is the new final vertex of each cone simplex. · OAI.Thomason.Construction.ConePrism.vertexMap
vertexModule def
The manuscript's actual right vertex projectives. · OAI.LittleFinitistic.QuadraticEncoding.vertexModule
vertexObject def
A vertex of a simplicial set gives an object in its categorification. · OAI.Thomason.Construction.NormalizedSimplexIdentities.vertexObject
vertexOrder def
The original darts precede all the newly added dummy darts. · OAI.MaxCutGames.Foundations.PCP.PreprocessingRegularTables.vertexOrder
vertexOrder def
Read the monotone vertex function of a strict functor into a poset. · OAI.Thomason.Construction.NormalizedSimplexIdentities.vertexOrder
vertexOrder def
The original darts precede all the newly added dummy darts. · OAI.UniqueGamesTheorem.Foundations.PCP.PreprocessingRegularTables.vertexOrder
vertexPaddingInTime def
Complete runtime certificate from the original input alone, with an explicit clean final frame and an actual polynomial in its encoded length. · OAI.MaxCutGames.Foundations.Complexity.MachineVertexPadding.vertexPaddingInTime
vertexPaddingInTime def
Complete runtime certificate from the original input alone, with an explicit clean final frame and an actual polynomial in its encoded length. · OAI.UniqueGamesTheorem.Foundations.Complexity.MachineVertexPadding.vertexPaddingInTime
vertexPairEq def
Agreement between the two labels of a normal pairing at a vertex. · OAI.Problem335.Pairings.vertexPairEq
vertexPoint def
A vertex of the simplex is also an honest point of its two-skeleton. · OAI.EilenbergGanea.LevelTransport.vertexPoint
vertexPoint def
The actual point of the realization represented by the greatest vertex. · OAI.Thomason.Construction.ConePrism.vertexPoint
vertexPotential def
The vertex summand, with Mathlib's log(0)=0 convention. · OAI.CliqueFreeIndependence.WeightedGraph.vertexPotential
vertexPotential def
The logarithm of the vertex product in tree:density. The first entry of m is the incoming edge exponent (zero at the root); the final entry equals one in the manuscript applications. · OAI.DilutedSpinGlass.PrescribedTree.vertexPotential
vertexProjection def
One summand of the separable diagonal projection. · OAI.LittleFinitistic.DirectedBound.DirectedSystem.vertexProjection
vertexQ def
The three actual images in the fixed quotient. · OAI.LittleFinitistic.QuadraticEncoding.vertexQ
vertexRanks def
Local vertex ranks are derived from the diagram, NOT additional rank hypotheses that might exclude one of its solutions. · OAI.IntegralCharacterVarieties.SurfacePresentation.Diagram.vertexRanks
vertexRaw def
Literal vertex classification: original vertices and the inserted face centers. · OAI.TorsionFreeZeroDivisors.ConedMap.vertexRaw
vertexRowBits def
Actual unary serialization of the complete vertex block. · OAI.MaxCutGames.Foundations.PCP.PoweringTableLayout.vertexRowBits
vertexRowBits def
Actual unary serialization of the complete vertex block. · OAI.UniqueGamesTheorem.Foundations.PCP.PoweringTableLayout.vertexRowBits
vertexRows def
Exactly the stored rows at positions B*v, ..., B*v+B-1. · OAI.MaxCutGames.Foundations.PCP.PoweringTableLayout.vertexRows
vertexRows def
A vertex emits every internal port, followed by its inherited port. · OAI.MaxCutGames.Foundations.PCP.PreprocessingRegularWords.vertexRows
vertexRows def
Exactly the stored rows at positions B*v, ..., B*v+B-1. · OAI.UniqueGamesTheorem.Foundations.PCP.PoweringTableLayout.vertexRows
vertexRows def
A vertex emits every internal port, followed by its inherited port. · OAI.UniqueGamesTheorem.Foundations.PCP.PreprocessingRegularWords.vertexRows
vertexRowWords def
All fields of these stored rows, in their actual codec order. · OAI.MaxCutGames.Foundations.PCP.PoweringTableLayout.vertexRowWords
vertexRowWords def
All fields of these stored rows, in their actual codec order. · OAI.UniqueGamesTheorem.Foundations.PCP.PoweringTableLayout.vertexRowWords
VertexRun structure
The complete inner loop for one vertex, starting at position zero. · OAI.MaxCutGames.Foundations.Complexity.MachineExpanderTable.VertexRun
VertexRun structure
The complete inner loop for one vertex, starting at position zero. · OAI.UniqueGamesTheorem.Foundations.Complexity.MachineExpanderTable.VertexRun
vertexScore def
First variation of the vertex product: one score for every uncontracted leaf, and gamma_beta times the score of a fresh path at every internal vertex. · OAI.DilutedSpinGlass.PrescribedTree.vertexScore
vertexSet def
A nondegenerate poset simplex is determined by its finite vertex set. · OAI.Thomason.Construction.PosetGeometry.vertexSet
vertexShares def
Vertex sharing means the same slot at one fixed stage boundary. · OAI.CoordinateSweeps.Grid.vertexShares
vertexSpace def
The vertex part is a submodule over A, hence retains both B-actions when A=B tensor B-op. · OAI.LittleFinitistic.OrdinarySimulation.Compression.vertexSpace
vertexSpace def
The vertex space e_i M(Y), as an actual k-subspace of the constructed module. · OAI.LittleFinitistic.QuadraticEncoding.Representation.vertexSpace
vertexSpaceScalarEquiv def
Change only the scalar description of the same actual vertex subspace. · OAI.LittleFinitistic.OrdinarySimulation.Compression.vertexSpaceScalarEquiv
vertexSpecialization def
Substitute x=y=t, leaving u,v as the two variables. · OAI.Paper170.vertexSpecialization
vertexStarHomotopy def
Restrict a simplicial homotopy fixing a vertex to its actual open star. This does not assert that the star is contractible for a general simplicial set. · OAI.Thomason.Construction.RealizationPrism.vertexStarHomotopy
vertexStarMap def
Restriction of an actual realized simplicial map to an open vertex star. · OAI.Thomason.Construction.RealizationPrism.vertexStarMap
VertexSuffixRun structure
A successful suffix of the finite position loop, returning actual finite state together with the execution certificate and its preserved caller. · OAI.MaxCutGames.Foundations.Complexity.MachineExpanderTable.VertexSuffixRun
VertexSuffixRun structure
A successful suffix of the finite position loop, returning actual finite state together with the execution certificate and its preserved caller. · OAI.UniqueGamesTheorem.Foundations.Complexity.MachineExpanderTable.VertexSuffixRun
VertexTable structure
One local vertex table. Every endpoint port has its own full ordered side list. A mate is a pairing of occurrences, not an identification of facets. · OAI.IntegralCharacterVarieties.OccurrenceIncidence.VertexTable
vertexTensorEquiv def
The genuine balanced tensor on a vertex projective evaluates to the original term. · OAI.LittleFinitistic.OrdinarySimulation.Compression.vertexTensorEquiv
vertexTensorEquiv def
The manuscript's E_i tensor_B M(Y) ≃ Y, for the actual right ideal E_i=e_iB. · OAI.LittleFinitistic.QuadraticEncoding.Representation.vertexTensorEquiv
vertexTime def
The actual fixed number of row commands multiplies the row polynomial. · OAI.MaxCutGames.Foundations.Complexity.PoweringPolynomialBudget.vertexTime
vertexTime def
The actual fixed number of row commands multiplies the row polynomial. · OAI.UniqueGamesTheorem.Foundations.Complexity.PoweringPolynomialBudget.vertexTime
vertexWitness def
Vertex-indexed opinions are tested at the two endpoints of the pivot dart. · OAI.MaxCutGames.Foundations.PCP.PoweringWitness.vertexWitness
vertexWitness def
Vertex-indexed opinions are tested at the two endpoints of the pivot dart. · OAI.UniqueGamesTheorem.Foundations.PCP.PoweringWitness.vertexWitness
vertical def
The vertical face applies the already defined inner differential, with exactly the totalization sign (-1)^i, then distributes the resulting finite sum. · OAI.DerivedBar.RecursiveTotal.vertical
vertical def
Signed vertical tensor differential on the concrete balanced tensor term. · OAI.LittleFinitistic.ComplexTensor.vertical
VerticalBound def
The upper-bound invariant on a set of heights, stated on differences because individual half-line indicators need not be integrable. · OAI.PlanarL1.Gluing.VerticalBound
verticalFiber def
Exact vertical section of the previously constructed conformal image. · OAI.SymmetricMahler.verticalFiber
verticalIdeal def
The vertical kernel of a surjective Lie subdirect product. · OAI.HarmonicCounterexample.Control.verticalIdeal
verticalOuter def
The vertical pair of horizontal composites. · OAI.Thomason.Construction.StrictOmegaCategory.GridGlobe.verticalOuter
verticalPath def
A vertical reference path for the fixed-scale support event. · OAI.SLEExactGauge.FirstHeightSupport.verticalPath
verticalPotential def
Primitive of the actual field between two graphs; no assigned derivative. · OAI.Bernoulli.Foliation.verticalPotential
verticalRadius def
The actual inverse radius in a vertical line of Omega. · OAI.SymmetricMahler.verticalRadius
verticalShear def
A shear does not change height and straightens an upward vector. · OAI.AffineBernstein.verticalShear
verticalTrace def
Straight vertical bridge, parametrized by height minus one. · OAI.CriticalHoneycomb.verticalTrace
verticalVariation def
The vertical velocity reconstructed from its normal part and horizontal part. · OAI.AffineBernstein.verticalVariation
vertices def
The two genuine product vertex sets embed into the common global radix space. Opposite sides cannot collide because the repetition count is positive. · OAI.MaxCutGames.Explicit.ProductPaddedOutput.vertices
vertices def
The non-isolated vertices of a finite edge family. · OAI.Problem313.SupportCombinatorics.vertices
vertices def
All vertices of a group-invariant collection of cubical flags. · OAI.SharpLiebThirring.CubeFlags.vertices
vertices def
Discard isolated ambient vertices as well as unused darts. · OAI.TorsionFreeZeroDivisors.SupportedImage.vertices
vertices def
The two genuine product vertex sets embed into the common global radix space. Opposite sides cannot collide because the repetition count is positive. · OAI.UniqueGamesTheorem.Explicit.ProductPaddedOutput.vertices
vHigh def
The degree-two part of the obstruction polynomial. · OAI.StableCoordinate.Obstruction.vHigh
view def
The relevant view of a physical stored value consists of its actual label-pair entries and its rational estimate. · OAI.ContingencyTables.CompanionPhaseFinishProgram.view
virtualCost def
Virtual movement under exactly the same finite hidden-state experiment. · OAI.KServer.HiddenMachine.virtualCost
visibleFallback def
A default actual projected answer depends only on the displayed positions. · OAI.MaxCutGames.Decoder.TransferredDecoding.visibleFallback
visibleFallback def
A default actual projected answer depends only on the displayed positions. · OAI.UniqueGamesTheorem.Decoder.TransferredDecoding.visibleFallback
visibleMap def
The precise visible table (T,A M), with the second component in its actual attainable range. The argument order is complement, hidden matrix. · OAI.MaxCutGames.Decoder.AdviceLaw.visibleMap
visibleMap def
The precise visible table (T,A M), with the second component in its actual attainable range. The argument order is complement, hidden matrix. · OAI.UniqueGamesTheorem.Decoder.AdviceLaw.visibleMap
visibleMass def
Probability of actual visible data carrying a transferred witness. · OAI.MaxCutGames.Decoder.ConstantSelection.visibleMass
visibleMass def
Probability of actual visible data carrying a transferred witness. · OAI.UniqueGamesTheorem.Decoder.ConstantSelection.visibleMass
visibleTau def
Read the shared homogeneous coordinate in the visible coordinate system. · OAI.MaxCutGames.Decoder.TableKeys.visibleTau
visibleTau def
Read the shared homogeneous coordinate in the visible coordinate system. · OAI.UniqueGamesTheorem.Decoder.TableKeys.visibleTau
visibleWitness def
Positive projected column-slice mass and sufficient conditional target agreement. Both quantities are computed after fixing actual visible data. · OAI.MaxCutGames.Decoder.VisibleTransfer.visibleWitness
visibleWitness def
Positive projected column-slice mass and sufficient conditional target agreement. Both quantities are computed after fixing actual visible data. · OAI.UniqueGamesTheorem.Decoder.VisibleTransfer.visibleWitness
visitCount def
Extended number of distinct visit times, defined by finite witnesses. · OAI.CircleDomainRigidity.visitCount
visitH def
project matrix of active key rays to one endpoint under attack · OAI.HadwigerCounterexample.Volley.visitH
Visits def
Vertices, including both endpoints, with no quotient of the edge data. · OAI.Superstring.Hierarchical.Path.Visits
visualArtinEquiv def
The visual splitting is an isomorphism with the genuine injective amalgamated free product of the two standard subgroups. · OAI.HarmonicArtin.ParabolicIntersections.visualArtinEquiv
vLayers def
The finite set of the V layers. · OAI.Problem335.BalancedSchedule.vLayers
vLow def
The degree-minus-one part of the obstruction polynomial. · OAI.StableCoordinate.Obstruction.vLow
VoiceS def
score service at another location.W-clock sufficient. power j normalizer. · OAI.ExactDerandomization.Cambria.Rime.Nest.VoiceS
Volley structure
One side of the lists, with actual point inputs, indexed by the simultaneous (both units') list positions. Tags passed separately because matched across the two sides. · OAI.HadwigerCounterexample.Volley
Voltage structure
An edge-voltage cocycle. Values off the edge set are immaterial. · OAI.HyperbolicObstruction.FinitePolyhedron.Voltage
voltage def
Every literal source relation gives a genuine topological voltage cover of its finite simplicial mapping-cylinder realization. · OAI.HyperbolicObstruction.FinitePolygonModel.Data.voltage
voltage def
The canonical cocycle of the finite edge presentation. · OAI.HyperbolicObstruction.FinitePolyhedron.EdgePresentation.voltage
voltage def
The actual triangle disks imply a group-valued flat cocycle. · OAI.HyperbolicObstruction.FinitePolyhedron.RootedPaths.voltage
volterra def
The actual Volterra integral for an operator-valued kernel and a source curve. · OAI.ForcedComputation.WeaklySingular.volterra
volumeMeasure def
Canonically normalized four-dimensional Riemannian volume, constructed from the actual length metric rather than an unspecified measure. · OAI.PositiveEinsteinFour.Geometry.volumeMeasure
volumeProduct def
The volume product minimized over the interior centers of the body. · OAI.GeneralMahler.volumeProduct
volumeRatio def
The volume ratio with the curvature-one round four-sphere. · OAI.PositiveEinsteinFour.Geometry.volumeRatio
vonNeumannCenter def
The center as a concrete von Neumann algebra. · OAI.KadisonSimilarity.vonNeumannCenter
vonNeumannIntersection def
The intersection of two concrete von Neumann algebras. · OAI.KadisonKastler.vonNeumannIntersection
vShift def
Small-angle link at V. · OAI.Release075.MarkedLineData.vShift