import GroupApproximation.Algebra.CoweightCoinvariants import GroupApproximation.Algebra.FaithfulRadicalCocycle import GroupApproximation.Algebra.MappingTelescope import GroupApproximation.Algebra.SemidirectProductAssoc import GroupApproximation.Algebra.TwoGeneratedFreeQuotient import GroupApproximation.Analysis.FaithfulTracialMatrix import GroupApproximation.Analysis.FiniteMatrixPositiveSquareRoot import GroupApproximation.Analysis.FiniteMatrixPositiveSquareRootUnit import GroupApproximation.Analysis.FiniteMatrixCorrectedStarEquiv import GroupApproximation.Analysis.FiniteProductCorrectedStarEquiv import GroupApproximation.Analysis.ProperIsometryFromCompression import GroupApproximation.Analysis.ExplicitReducedGroupCStarConsequences import GroupApproximation.Analysis.MaximalGroupCStar import GroupApproximation.Analysis.UniversalCStarHNN import GroupApproximation.Analysis.MaximalCStarKazhdanAverage import GroupApproximation.Analysis.QuasiRegularWitness import GroupApproximation.Analysis.StateExtension import GroupApproximation.Analysis.SpectralStateWitness import GroupApproximation.Analysis.SpectralComponentDiameter import GroupApproximation.Analysis.SpectralComponentMotion import GroupApproximation.Analysis.ClopenSpectralProjection import GroupApproximation.Analysis.GNSEigenvector import GroupApproximation.Computability.AbelianEnumeratedPi02 import GroupApproximation.Computability.ArithmeticalLedgerEndpoint import GroupApproximation.Computability.ElementaryEnumeratedHardness import GroupApproximation.Computability.FreeSubgroupEnumeratedHardness import GroupApproximation.Computability.HyperlinearEnumeratedHardness import GroupApproximation.Computability.HyperlinearUndecidabilityRoute import GroupApproximation.Computability.AmenableEnumeratedHardness import GroupApproximation.Computability.IsoInvariantSwitchHardness import GroupApproximation.Computability.LEFEnumeratedPi02 import GroupApproximation.Computability.MFEnumeratedMicrostate import GroupApproximation.Computability.MFEnumeratedNormalForm import GroupApproximation.Computability.MFEnumeratedPi02 import GroupApproximation.Computability.PerfectEnumeratedHardness import GroupApproximation.Computability.PerfectEnumeratedPi02 import GroupApproximation.Computability.ProfinitelyClosedIndexSet import GroupApproximation.Computability.RFEnumeratedHardness import GroupApproximation.Computability.RFPresentationPi02 import GroupApproximation.Computability.RFRecognitionHierarchy import GroupApproximation.Computability.SoficEnumeratedPi02 import GroupApproximation.Computability.SoficMicrostateNormalForm import GroupApproximation.Computability.SoficRecognitionPi02 import GroupApproximation.Computability.TorsionFreeEnumeratedHardness import GroupApproximation.Computability.TorsionFreeEnumeratedPi02 import GroupApproximation.Computability.TrivialEnumeratedPi02 import GroupApproximation.Kazhdan.KazhdanEigenvalueBound import GroupApproximation.Analysis.AbstractSpectralGap import GroupApproximation.Analysis.CStarSpectralProjection import GroupApproximation.Analysis.KazhdanProjectionAbsorption import GroupApproximation.Analysis.KazhdanProjectionOneSidedOrder import GroupApproximation.Analysis.ProjectionOrbitCollapse import GroupApproximation.Analysis.CollapseJoinNonvanishing import GroupApproximation.Analysis.CollapseNormalizedSetup import GroupApproximation.Analysis.CollapseUnitaryLift import GroupApproximation.Analysis.GroupStandardFormInstance import GroupApproximation.Analysis.GroupVonNeumannAlgebra import GroupApproximation.Analysis.GroupVonNeumannTrace import GroupApproximation.Analysis.LimitsTraceStandardForm import GroupApproximation.Analysis.PrintedFiniteDimensionalUses import GroupApproximation.Analysis.PermutationICC import GroupApproximation.Analysis.ShiftIsometry import GroupApproximation.Analysis.TwoSidedRegularCommutant import GroupApproximation.Analysis.MaximalCStarProperCompression import GroupApproximation.Analysis.AmenableQuasidiagonal import GroupApproximation.Analysis.CStarExactness import GroupApproximation.Analysis.NFAlgebra import GroupApproximation.Analysis.CStarMatrixFactorization import GroupApproximation.Analysis.LanceMatrixSubalgebra import GroupApproximation.Analysis.LanceBlockOperator import GroupApproximation.Analysis.LanceChoiFunctional import GroupApproximation.Analysis.LanceHermitianFunctional import GroupApproximation.Analysis.LanceMatrixArveson import GroupApproximation.Analysis.LanceDayEngine import GroupApproximation.Analysis.LanceMultiplicationOperator import GroupApproximation.Analysis.LanceHypertrace import GroupApproximation.Analysis.LanceCPApprox import GroupApproximation.Analysis.LanceCPContractiveUnitalization import GroupApproximation.Analysis.LanceNuclearity import GroupApproximation.Kazhdan.KazhdanUniverseDescent import GroupApproximation.Sofic.ChosenMaximalCStarInfinite import GroupApproximation.Sofic.FreeGroupPFFInterface import GroupApproximation.Analysis.TorsionFreeFullMFCStarConsequences import GroupApproximation.Computability.MarkovMFConsequences import GroupApproximation.Computability.MFRadicalComputer import GroupApproximation.Computability.MFRadicalQuine import GroupApproximation.Computability.MFRadicalQuineSource import GroupApproximation.Computability.MFRadicalGodel import GroupApproximation.Computability.MFObserverBlindPromise import GroupApproximation.Endpoint.MFObserverBlindPromiseAudit import GroupApproximation.Computability.OperatorMFMarkovWitness import GroupApproximation.Computability.CStarRecognitionConsequences import GroupApproximation.Computability.PresentationCodes import GroupApproximation.Computability.PresentationCodeCompleteness import GroupApproximation.Computability.PresentationCodeList import GroupApproximation.Computability.RabinVariantCode import GroupApproximation.Computability.CoprodCode import GroupApproximation.Computability.AmalgamCode import GroupApproximation.Computability.AmalgamCodeSemantics import GroupApproximation.Computability.AmalgamCodePushout import GroupApproximation.Computability.BenignMapEmbCode import GroupApproximation.Computability.BenignInfCode import GroupApproximation.Computability.BenignInfCodeSemantics import GroupApproximation.Computability.BenignSupCode import GroupApproximation.Computability.BenignComapCode import GroupApproximation.Computability.BenignComapThreeCode import GroupApproximation.Computability.CodedProfiniteWitnessThree import GroupApproximation.Computability.BenignMapEmbRopeInput import GroupApproximation.Computability.DirectProductCodeSemantics import GroupApproximation.Computability.AdianRabinVariantTransform import GroupApproximation.Computability.RawWord import GroupApproximation.Computability.RawTransform import GroupApproximation.Computability.RawTransformPrimrec import GroupApproximation.Computability.OperatorMFMarkovAtCodes import GroupApproximation.Computability.StringRewriting import GroupApproximation.Computability.UniversalCodeHalting import GroupApproximation.Computability.UniversalCode import GroupApproximation.Computability.RewriteMonoid import GroupApproximation.Computability.RewriteInvariants import GroupApproximation.Computability.RewriteConfluence import GroupApproximation.Computability.AdianRabinMarkovProperty import GroupApproximation.Computability.WordProblemRE import GroupApproximation.GroupTheory.FiniteWordAutomaton import GroupApproximation.GroupTheory.FiniteRelatorQuotient import GroupApproximation.GroupTheory.QuotientProtectedPair import GroupApproximation.GroupTheory.TreeGraphGeometry import GroupApproximation.Sofic.AdjointMatrix import GroupApproximation.Sofic.HilbertUltraproductFaithful import GroupApproximation.Sofic.HilbertUltraproductSeparating import GroupApproximation.Sofic.KOmegaHilbert import GroupApproximation.Sofic.OmegaOperatorUltraproduct import GroupApproximation.Sofic.OmegaAlmostRepresentation import GroupApproximation.Sofic.OmegaCoronaFinite import GroupApproximation.Sofic.OmegaKazhdanCompression import GroupApproximation.Sofic.OmegaWeightedAmbient import GroupApproximation.Sofic.UltrafilterSubsequence import GroupApproximation.Sofic.HilbertUltraproductSpace import GroupApproximation.Sofic.ProjectionRankFlip import GroupApproximation.Sofic.ExactInvolutionCut import GroupApproximation.Sofic.InvolutiveTwoSheet import GroupApproximation.Sofic.PauliBranchTransfer import GroupApproximation.Sofic.DoublePauliCoefficient import GroupApproximation.Sofic.TransitionGaugeInvariance import GroupApproximation.Sofic.CoefficientAlternatingReynolds import GroupApproximation.Sofic.MixedCommutatorDihedral import GroupApproximation.Sofic.SpectralCapture import GroupApproximation.Sofic.NegativeCornerModel import GroupApproximation.Sofic.BlockCliffordLamp import GroupApproximation.Sofic.BlockingFamilyRadical import GroupApproximation.Sofic.CliffordLampGroup import GroupApproximation.Monsters.AffineSL3Doubling import GroupApproximation.Monsters.CliffordAlgebraLamp import GroupApproximation.Monsters.CliffordLampLocallyFinite import GroupApproximation.Monsters.AffineSL3Scaling import GroupApproximation.Monsters.ExplicitLinearModel import GroupApproximation.Monsters.ExplicitLinearModelScaling import GroupApproximation.Monsters.CyclicBaseCalibration import GroupApproximation.Monsters.LiteralCyclicCalibration import GroupApproximation.Monsters.LiteralCyclicRelatorCount import GroupApproximation.Monsters.LiteralP13MatrixModel import GroupApproximation.Monsters.SL3ElementaryGeneration import GroupApproximation.Monsters.P13SteinbergCalculus import GroupApproximation.Monsters.P13UnipotentInjectivity import GroupApproximation.Monsters.P13WeylCalculus import GroupApproximation.Monsters.P13Weyl23Calculus import GroupApproximation.Monsters.P13Weyl13Calculus import GroupApproximation.Monsters.P13WeylFourthPowers import GroupApproximation.Monsters.P13SL2ComparisonAll import GroupApproximation.Monsters.SL3BlockEmbeddingAll import GroupApproximation.Monsters.P13ParabolicKernel import GroupApproximation.Monsters.P13ColumnLift import GroupApproximation.Monsters.P13MonomialMachine import GroupApproximation.Monsters.P13DescentCore import GroupApproximation.Monsters.P13WordDescent import GroupApproximation.Monsters.P13DescentCases import GroupApproximation.Monsters.P13Completeness import GroupApproximation.Monsters.P13DescentMaster import GroupApproximation.Monsters.LiteralBaseResiduallyFinite import GroupApproximation.Monsters.P13LowerUnipotentInjectivity import GroupApproximation.Monsters.SL2BraidPresentation import GroupApproximation.Monsters.P13SL2Comparison import GroupApproximation.Monsters.SL3BlockEmbedding import GroupApproximation.Monsters.SL2WeylRelations import GroupApproximation.Monsters.MoebiusIrrationalAction import GroupApproximation.GroupTheory.FiniteCyclicHom import GroupApproximation.GroupTheory.HNNBrittonPinch import GroupApproximation.GroupTheory.HNNBrittonSpelling import GroupApproximation.GroupTheory.HNNBrittonCyclic import GroupApproximation.GroupTheory.FiniteHNNFreeLabelAction import GroupApproximation.GroupTheory.FiniteHNNFreeLabelFaithful import GroupApproximation.GroupTheory.FiniteHNNResiduallyFinite import GroupApproximation.Monsters.SL2PingPong import GroupApproximation.Monsters.SL2Completeness import GroupApproximation.Monsters.P13BlockSL2 import GroupApproximation.Monsters.CyclicBaseLEFObstruction import GroupApproximation.Sofic.ScalingFamilyPresentation import GroupApproximation.Sofic.ScalingFamilyRelatorCount import GroupApproximation.Sofic.ScalingFamilyLinearWitness import GroupApproximation.Sofic.ScalingFamilyEndpoint import GroupApproximation.Sofic.LiteralNonMFLinearWitness import GroupApproximation.Sofic.WitnessVerticalResiduallyFinite import GroupApproximation.Sofic.AlternatingLampVisibleQuotient import GroupApproximation.Sofic.LiteralNonMFEndpoint import GroupApproximation.Sofic.LiteralBaseTranslationLattice import GroupApproximation.Sofic.LiteralBaseDoublingIndex import GroupApproximation.Sofic.LiteralBaseP13Replay import GroupApproximation.Sofic.LiteralBasePropertyTBridge import GroupApproximation.Sofic.LiteralBaseTwoGenerator import GroupApproximation.Sofic.LiteralFiniteDimensionalObstruction import GroupApproximation.Sofic.LiteralUniversalHorn import GroupApproximation.Sofic.LiteralPresentationRadius import GroupApproximation.Sofic.LiteralMarkedCylinderTopology import GroupApproximation.Sofic.LiteralMarkedCylinder import GroupApproximation.Sofic.LiteralSixGenerator import GroupApproximation.Sofic.LiteralSignFreeQuotient import GroupApproximation.Sofic.LiteralTietzePresentation import GroupApproximation.Sofic.LiteralWitnessConsequences import GroupApproximation.Sofic.MarkedCompressionInclusionData import GroupApproximation.Sofic.CompressionDefectSquare import GroupApproximation.Sofic.MarkedCompressionGroup import GroupApproximation.Sofic.ChosenMarkedCylinder import GroupApproximation.Sofic.ChosenUniversalHorn import GroupApproximation.Sofic.KazhdanCompressorCorner import GroupApproximation.Sofic.MarkedCompressionVectorChain import GroupApproximation.Sofic.MarkedCompressionSequentialKill import GroupApproximation.Sofic.MarkedCompressionRootCapture import GroupApproximation.Sofic.FiniteNormalAverageCorner import GroupApproximation.Sofic.FiniteNormalCompressionObstruction import GroupApproximation.Sofic.FiniteNormalCoronaObstruction import GroupApproximation.Sofic.OperatorMF import GroupApproximation.Sofic.CDEOperatorMF import GroupApproximation.Sofic.MFDefinitions import GroupApproximation.Sofic.MFRepresentationVariants import GroupApproximation.Sofic.CDEMFRadical import GroupApproximation.Sofic.RadicalSeparation import GroupApproximation.Sofic.NormMFUniversalQuotient import GroupApproximation.Sofic.NormMFUniversalCorona import GroupApproximation.Sofic.NormMFCoronaRadical import GroupApproximation.Sofic.NormMFPrintedConsequences import GroupApproximation.Sofic.NormallyGeneratedMFObstruction import GroupApproximation.Sofic.OperatorMFPositiveControls import GroupApproximation.Sofic.OperatorMFProduct import GroupApproximation.Sofic.OperatorMFHNNCyclicBlocks import GroupApproximation.Sofic.LocallyFiniteMF import GroupApproximation.Sofic.CentralInvolutionFinite import GroupApproximation.Sofic.OperatorMFQuotientNonclosure import GroupApproximation.Sofic.OperatorMFFreeProductConsequences import GroupApproximation.Computability.SeededSelfAwareMFCompiler import GroupApproximation.Sofic.MarkedCompressionProperness import GroupApproximation.Sofic.ChosenMarkedPresentation import GroupApproximation.Sofic.ChosenNonMFTheorem import GroupApproximation.Endpoint.ChosenNonMFAudit import GroupApproximation.Endpoint.SignFreeCompressionAudit import GroupApproximation.Sofic.ChosenNonMFEndpoint import GroupApproximation.Sofic.NormUltraproductSequentialExtraction import GroupApproximation.Sofic.NormMFConsequences import GroupApproximation.Sofic.Asymptotics import GroupApproximation.Sofic.ExteriorMFProfile import GroupApproximation.Sofic.UnitaryProjectionBalance import GroupApproximation.Sofic.ExplicitNonMFBase import GroupApproximation.Steinberg.QuotientExactness import GroupApproximation.Domination.Audit import GroupApproximation.Sofic.AlmostAutomorphism import GroupApproximation.PropertyT.A2System import GroupApproximation.PropertyT.A2ClassTwoOrthogonality import GroupApproximation.PropertyT.A2MagicGraph import GroupApproximation.PropertyT.A2MagicGraphEstimates import GroupApproximation.PropertyT.A2MagicLaplacian import GroupApproximation.PropertyT.A2MagicEnergy import GroupApproximation.PropertyT.A2MagicHilbert import GroupApproximation.Kazhdan.PositiveOperatorGap import GroupApproximation.Kazhdan.ExactHodgeCertificate import GroupApproximation.Sofic.LiteralBaseP13RotationQuotient import GroupApproximation.PropertyT.FreeAlgebraDegree import GroupApproximation.PropertyT.FreeRootFiltration import GroupApproximation.PropertyT.FreeRootActions import GroupApproximation.PropertyT.FreeRootPlane import GroupApproximation.PropertyT.FreeRootPlaneMassBase import GroupApproximation.PropertyT.FreeRootPlaneMass import GroupApproximation.PropertyT.FreeRootFunctionalValuation import GroupApproximation.PropertyT.FreeRootPlaneFourier import GroupApproximation.PropertyT.FreeRootCharacterValuationBase import GroupApproximation.PropertyT.FreeRootCharacterValuation import GroupApproximation.PropertyT.FiniteFieldElementaryPropertyT import GroupApproximation.PropertyT.FreeElementaryPropertyT import GroupApproximation.PropertyT.FiniteTypeCharacteristicTwoPropertyT import GroupApproximation.Leavitt.FiniteFieldLeavitt import GroupApproximation.PropertyT.A2Kazhdan import GroupApproximation.PropertyT.ClassTwoNormalForm import GroupApproximation.PropertyT.ClassTwoApproximation import GroupApproximation.Matching.DirectedCoarea import GroupApproximation.Kazhdan.KazhdanImprovement import GroupApproximation.Kazhdan.Kazhdan import GroupApproximation.Kazhdan.KazhdanDisplacementCriterion import GroupApproximation.Kazhdan.HilbertComplexification import GroupApproximation.Kazhdan.KazhdanComplex import GroupApproximation.Kazhdan.KazhdanUniverse import GroupApproximation.Kazhdan.KazhdanFiniteGeneration import GroupApproximation.PropertyT.CharacterMass import GroupApproximation.Leavitt.RankTwoCompression import GroupApproximation.Kazhdan.KazhdanControl import GroupApproximation.Kazhdan.AlmostMinimalDisplacement import GroupApproximation.Kazhdan.DelormeFixedPoint import GroupApproximation.Kazhdan.ShalomFinitePresentation import GroupApproximation.Kazhdan.UltralimitGeometry import GroupApproximation.Kazhdan.UltralimitGaussianBoundedness import GroupApproximation.Kazhdan.GaussianPositiveDefinite import GroupApproximation.Kazhdan.HilbertCircumcenter import GroupApproximation.Kazhdan.KazhdanFixedSpace import GroupApproximation.Kazhdan.HilbertConvexFixedPoint import GroupApproximation.PropertyT.InvolutionSplitting import GroupApproximation.PropertyT.FiniteInvolutionDecomposition import GroupApproximation.Kazhdan.HilbertEpsilonOrthogonality import GroupApproximation.PropertyT.FiniteGroupAverage import GroupApproximation.PropertyT.FiniteOrbitRepresentation import GroupApproximation.PropertyT.FiniteClassTwoOrthogonality import GroupApproximation.PropertyT.OrthogonalRepresentationDecomposition import GroupApproximation.PropertyT.FiniteClassTwoDecompositionBound import GroupApproximation.PropertyT.ClassTwoOrthogonality import GroupApproximation.PropertyT.NormalEdgeCodistance import GroupApproximation.Kazhdan.KazhdanGenerators import GroupApproximation.Kazhdan.KazhdanOrthogonal import GroupApproximation.Kazhdan.FixedSpaceCompression import GroupApproximation.Kazhdan.FixedSpaceStabilizer import GroupApproximation.Kazhdan.FixedSpaceDefect import GroupApproximation.Kazhdan.KazhdanProjection import GroupApproximation.Kazhdan.InvariantDisplacement import GroupApproximation.Kazhdan.KazhdanFiniteModel import GroupApproximation.Kazhdan.KazhdanGNS import GroupApproximation.Kun.KunFiniteMarkov import GroupApproximation.Kun.KunBoundary import GroupApproximation.Kun.KunRounding import GroupApproximation.Kun.KunThreshold import GroupApproximation.Kun.KunGeneratorGraph import GroupApproximation.Kun.KunSupport import GroupApproximation.Kun.KunIndicatorRounding import GroupApproximation.Kun.KunQuantitativeRounding import GroupApproximation.Kun.KunRemoval import GroupApproximation.Kun.KunAsymptoticRemoval import GroupApproximation.Kun.KunSmallBoundary import GroupApproximation.Kun.KunPartition import GroupApproximation.Kun.KunFinitePartition import GroupApproximation.Kun.KunDiagonalPartition import GroupApproximation.Kun.KunDecomposition import GroupApproximation.Kun.KunFixedDecomposition import GroupApproximation.KunThom.KunThomDiagonal import GroupApproximation.KunThom.KunThomCorrelation import GroupApproximation.KunThom.KunThomFiniteMarkov import GroupApproximation.KunThom.KunThomRounding import GroupApproximation.KunThom.KunThomParameters import GroupApproximation.KunThom.KunThomTheorem import GroupApproximation.Kun.KunSpectralCounterexample import GroupApproximation.Matching.MaximalCutRepair import GroupApproximation.Sofic.SoficRestriction import GroupApproximation.Sofic.IntersectionReduction import GroupApproximation.Sofic.RelativeIntersectionPermanence import GroupApproximation.Matching.EssentialExpanderRepair import GroupApproximation.KunThom.KunThomEssential import GroupApproximation.Kun.KunPartitionBoundary import GroupApproximation.Kun.KunPartitionCrossing import GroupApproximation.Kun.KunBlockGraph import GroupApproximation.Kun.KunRepairGraph import GroupApproximation.Kun.KunMarkerSelection import GroupApproximation.Kun.KunLocalNeighborhood import GroupApproximation.Kun.KunBadBlocks import GroupApproximation.Kun.KunSelectiveRepairGraph import GroupApproximation.Kun.KunSelectiveRepairExpansion import GroupApproximation.Kun.KunRefinedInvariance import GroupApproximation.Kun.KunRepairExpansion import GroupApproximation.Kun.KunUniformMovement import GroupApproximation.Kun.KunUniformRemoval import GroupApproximation.Kun.KunUniformRounding import GroupApproximation.Kun.KunUniformDecompositionStep import GroupApproximation.Criterion.CompressionSetup import GroupApproximation.Criterion.ExactCompression import GroupApproximation.Criterion.ChainConditionCompression import GroupApproximation.Criterion.TensorInvariantRigidity import GroupApproximation.Criterion.ClosedEnvelopeCompression import GroupApproximation.Criterion.CommutantRigidity import GroupApproximation.Criterion.CompressionCentralizerDefect import GroupApproximation.Sofic.NormMFResidualExactQuotient import GroupApproximation.Sofic.IntrinsicCompressionDefect import GroupApproximation.Sofic.KazhdanAsymptoticCommutant import GroupApproximation.Sofic.ScaledKazhdanTransport import GroupApproximation.Sofic.IntertwinerKazhdanTransport import GroupApproximation.Sofic.TorsionCompressionCollapse import GroupApproximation.Sofic.MFRelationClosure import GroupApproximation.Sofic.MFTraceRecognition import GroupApproximation.Sofic.InvolutionRankMass import GroupApproximation.Sofic.CollisionCapacityDetectors import GroupApproximation.Sofic.ExactInvolutionLifts import GroupApproximation.Kazhdan.ApproximateCircumcenter import GroupApproximation.Sofic.InvolutionMicrostateTools import GroupApproximation.Sofic.InvolutionOrbitMicrostates import GroupApproximation.Sofic.InvolutionCollapseMetric import GroupApproximation.Sofic.InvolutionCollapseProfile import GroupApproximation.Sofic.InvolutionCollapseCocycle import GroupApproximation.Sofic.InvolutionCollapseCenter import GroupApproximation.Sofic.InvolutionCollapseIndexCapture import GroupApproximation.Sofic.InvolutionCollapseEndpointPrep import GroupApproximation.Sofic.InvolutionCollapseEndpoint import GroupApproximation.Sofic.ProjectionCompressionCollapse import GroupApproximation.Sofic.SpectralCompression import GroupApproximation.Manuscript.SpectralPaper.MainTheorems import GroupApproximation.Manuscript.SpectralPaper.Audit import GroupApproximation.Sofic.TorsionSpectralCollapse import GroupApproximation.Sofic.TorsionActiveCore import GroupApproximation.Sofic.FiniteOrderRankMass import GroupApproximation.Sofic.ActiveCoreAlmostRepresentation import GroupApproximation.Sofic.FiniteOrderNormalGenerator import GroupApproximation.Sofic.SimpleTorsionDichotomy import GroupApproximation.Sofic.MatricialStabilityRadical import GroupApproximation.Sofic.PropertyTFreeMFCollapse import GroupApproximation.Sofic.CommutingLampCollapse import GroupApproximation.Sofic.CommutingLampQuotientSofic import GroupApproximation.Algebra.HNNTorsionFree import GroupApproximation.Sofic.GreendlingerCombinatorics import GroupApproximation.Sofic.GreendlingerConjugation import GroupApproximation.Sofic.GreendlingerNormalForm import GroupApproximation.Sofic.GreendlingerOneRelator import GroupApproximation.Sofic.GreendlingerExpression import GroupApproximation.Sofic.GreendlingerCancellation import GroupApproximation.Sofic.GreendlingerDescent import GroupApproximation.Sofic.GreendlingerPiece import GroupApproximation.Sofic.IntegerLampSurvival import GroupApproximation.Monsters.LiteralBaseCompleteness import GroupApproximation.Sofic.LEFMarkedCompression import GroupApproximation.Algebra.FinitePresentationTietze import GroupApproximation.Algebra.PartialCommutationLamp import GroupApproximation.Algebra.FiniteResidual import GroupApproximation.Algebra.VisibleQuotient import GroupApproximation.Algebra.FiniteResidualCommensurability import GroupApproximation.Algebra.AlternatingLampNoncommensurable import GroupApproximation.Algebra.TorsionFreeRank import GroupApproximation.Algebra.AmenableMFProof import GroupApproximation.Algebra.PermutationalWreath import GroupApproximation.Algebra.PermutationalWreathSimple import GroupApproximation.Algebra.PermutationalWreathAmenable import GroupApproximation.Algebra.PermutationalWreathLinear import GroupApproximation.Algebra.AbelianLampPushforward import GroupApproximation.Algebra.AbelianLampTelescopeKernel import GroupApproximation.Algebra.PermutationalWreathRadicalTame import GroupApproximation.Algebra.WreathLampPushforward import GroupApproximation.Algebra.WreathTelescopeUnion import GroupApproximation.Algebra.IntJacobson import GroupApproximation.Algebra.FiniteTypeField import GroupApproximation.Algebra.Malcev import GroupApproximation.Algebra.MalcevLinear import GroupApproximation.Algebra.WreathSplitQuotient import GroupApproximation.Algebra.PerfectLamp import GroupApproximation.Algebra.ModTwoLampParity import GroupApproximation.Sofic.FiniteDimensionalResidual import GroupApproximation.Sofic.ThreeRadicalsCoincide import GroupApproximation.Sofic.LinearResidual import GroupApproximation.Sofic.FourRadicalsCoincide import GroupApproximation.Sofic.FiveRadicalsCoincide import GroupApproximation.Sofic.BlockAmplificationRepair import GroupApproximation.Sofic.AmplifiedBlockNorms import GroupApproximation.Sofic.InducedCoronaMF import GroupApproximation.Sofic.SoficPiProduct import GroupApproximation.Sofic.AmenableActionSofic import GroupApproximation.Sofic.CoAmenableActionSofic import GroupApproximation.Sofic.WreathPermLayer import GroupApproximation.Sofic.WreathChartLamp import GroupApproximation.Sofic.GeneralizedWreathSofic import GroupApproximation.Sofic.AscendingHNNWreathSofic import GroupApproximation.Sofic.RegularActionSofic import GroupApproximation.Algebra.WreathTelescopeTower import GroupApproximation.Algebra.WreathFunctor import GroupApproximation.Algebra.GraphProduct import GroupApproximation.Algebra.GraphProductAction import GroupApproximation.Analysis.PeterWeylProfinite import GroupApproximation.Analysis.CompactHaar import GroupApproximation.Analysis.CompactIntegralOperator import GroupApproximation.Algebra.TietzeFinitePresentation import GroupApproximation.Algebra.FinitePresentationKernel import GroupApproximation.Sofic.FiniteIndexRigidity import GroupApproximation.Algebra.FreePermutationalPrecursor import GroupApproximation.Algebra.FreePrecursorUniversal import GroupApproximation.Algebra.FreePrecursorPresentation import GroupApproximation.Sofic.UniversalFactorization import GroupApproximation.Sofic.RadicalFunctoriality import GroupApproximation.Algebra.SplitExtensionFailure import GroupApproximation.Sofic.SplitExtensionEndpoint import GroupApproximation.Sofic.CommensurabilityInvariance import GroupApproximation.Sofic.Type0Transfer import GroupApproximation.Sofic.FiniteIndexNonMF import GroupApproximation.Sofic.DossierAuditAddenda import GroupApproximation.Sofic.SoficNonMFAssembly import GroupApproximation.Sofic.SoficActionOrbits import GroupApproximation.Sofic.SoficActionApproximationBelow import GroupApproximation.Sofic.AscendingHNNFolner import GroupApproximation.Sofic.AscendingHNNDiagonalOrbits import GroupApproximation.Sofic.TargetEquivalence import GroupApproximation.Sofic.InducedFiniteDimensional import GroupApproximation.Kazhdan.IntegerNotKazhdan import GroupApproximation.Sofic.SoficAction import GroupApproximation.Sofic.SoficActionEmbedding import GroupApproximation.Sofic.AscendingHNNSoficDescent import GroupApproximation.Sofic.SoficActionFiniteOrbits import GroupApproximation.Sofic.SoficActionExamples import GroupApproximation.Sofic.MaxDisplacement import GroupApproximation.Sofic.CoronaSubsequence import GroupApproximation.Sofic.CyclicStack import GroupApproximation.Sofic.SoficActionCyclicExtension import GroupApproximation.Sofic.AscendingHNNNotKazhdan import GroupApproximation.Sofic.AscendingHNNCosetActionSofic import GroupApproximation.Sofic.SoficActionChabauty import GroupApproximation.Sofic.SoficActionSum import GroupApproximation.Sofic.AscendingHNNStabilizer import GroupApproximation.Sofic.AscendingHNNDoubleCosets import GroupApproximation.Sofic.AscendingHNNWreathWitness import GroupApproximation.Sofic.AscendingHNNSplitExtension import GroupApproximation.Sofic.AscendingHNNTelescopeRadical import GroupApproximation.Sofic.AscendingHNNFullTelescopeRadical import GroupApproximation.Sofic.PerfectLampCompressionRadical import GroupApproximation.Sofic.CompressionWreathFinitelyGenerated import GroupApproximation.Sofic.AlternatingLampExactRadical import GroupApproximation.Sofic.FinitePerfectLampExactRadical import GroupApproximation.Sofic.AlternatingLampBohrResidual import GroupApproximation.Manuscript.MFRadicals.Definitions import GroupApproximation.Manuscript.MFRadicals.SemanticClosure import GroupApproximation.Manuscript.MFRadicals.Compression import GroupApproximation.Manuscript.MFRadicals.ExplicitSeed import GroupApproximation.Manuscript.MFRadicals.FullRadical import GroupApproximation.Manuscript.MFRadicals.SimpleSofic import GroupApproximation.Manuscript.MFRadicals.PerfectLampExact import GroupApproximation.Manuscript.MFRadicals.AlternatingFamily import GroupApproximation.Manuscript.MFRadicals.RadicalComputer import GroupApproximation.Manuscript.MFRadicals.FinitePerfectLamp import GroupApproximation.Manuscript.MFRadicals.TargetEquivalence import GroupApproximation.Manuscript.MFRadicals.MainTheorems import GroupApproximation.Manuscript.OneSidedMFRadical.LiteralMFClosure import GroupApproximation.Manuscript.OneSidedMFRadical.ResidualCalculus import GroupApproximation.Manuscript.OneSidedMFRadical.FiniteDimensionalCommutant import GroupApproximation.Manuscript.OneSidedMFRadical.StableFiniteness import GroupApproximation.Manuscript.OneSidedMFRadical.UniversalFactorization import GroupApproximation.Manuscript.OneSidedMFRadical.PrescribedQuotients import GroupApproximation.Manuscript.OneSidedMFRadical.ClosurePullback import GroupApproximation.Manuscript.OneSidedMFRadical.DefectHS import GroupApproximation.Manuscript.OneSidedMFRadical.KazhdanTransport import GroupApproximation.Manuscript.OneSidedMFRadical.NormalKazhdan import GroupApproximation.Manuscript.OneSidedMFRadical.KazhdanProjectionOrder import GroupApproximation.Manuscript.OneSidedMFRadical.KazhdanProjectionOrderLiteral import GroupApproximation.Manuscript.OneSidedMFRadical.CentralCoronaCorner import GroupApproximation.Manuscript.OneSidedMFRadical.CompressionCriterion import GroupApproximation.Manuscript.OneSidedMFRadical.DefectSaturation import GroupApproximation.Manuscript.OneSidedMFRadical.ShadowResidual import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedDefectShadow import GroupApproximation.Manuscript.OneSidedMFRadical.Audit import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedDefect import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedCriterion import GroupApproximation.Manuscript.OneSidedMFRadical.CurrentManuscriptDefinitionRepairs import GroupApproximation.Manuscript.NonMF.LiteralEDirectCriterion import GroupApproximation.Manuscript.NonMF.SimpleInDefect import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedAudit import GroupApproximation.Manuscript.OneSidedMFRadical.RankTwelveConfiguration import GroupApproximation.Manuscript.OneSidedMFRadical.RankTwelveEJZInstance import GroupApproximation.Manuscript.OneSidedMFRadical.RankTwelveAudit import GroupApproximation.Manuscript.OneSidedMFRadical.RankTwelveSimplicity import GroupApproximation.Endpoint.MFRadicalPaperAudit import GroupApproximation.Sofic.TelescopeLimitKernel import GroupApproximation.Sofic.ProfiniteTwins import GroupApproximation.Sofic.AlternatingLampLiteralPackage import GroupApproximation.Sofic.LiteralDoublingWreathNonMF import GroupApproximation.Sofic.CoronaRadicalPullback import GroupApproximation.Sofic.MoverGeneration import GroupApproximation.Sofic.HereditaryNonsoficDescent import GroupApproximation.Sofic.SmallCancellationRouter import GroupApproximation.Sofic.ConcreteCompressionSource import GroupApproximation.Sofic.DefectSaturation import GroupApproximation.Sofic.KazhdanSignCriterion import GroupApproximation.Sofic.IntrinsicCompressionMFRadical import GroupApproximation.Sofic.UltraproductAdjointAmbient import GroupApproximation.Sofic.UltraproductDedekindFinite import GroupApproximation.Sofic.UltraproductKazhdanProjection import GroupApproximation.Sofic.UltraproductKazhdanTransport import GroupApproximation.Sofic.ManuscriptKazhdanTransport import GroupApproximation.Sofic.KazhdanTransportAnyUniverse import GroupApproximation.Sofic.NormalKazhdanCompressionObstruction import GroupApproximation.Sofic.KazhdanCompressionFunctorial import GroupApproximation.Sofic.NormalKazhdanMFRadical import GroupApproximation.Sofic.NormalKazhdanHyperlinearKilled import GroupApproximation.Sofic.CoronaImageNormalKazhdan import GroupApproximation.Sofic.QuestionTwoReduction import GroupApproximation.Sofic.TorsionFreeFullMFRadical import GroupApproximation.Sofic.OpToHSShadowResidual import GroupApproximation.Sofic.TorsionFreeFullMFConsequences import GroupApproximation.Sofic.TensorPowerAmplification import GroupApproximation.Sofic.TensorPowerTransport import GroupApproximation.Algebra.ProductFinitePresentation import GroupApproximation.Algebra.Amenable import GroupApproximation.Algebra.AmenableMean import GroupApproximation.Algebra.AmenableInt import GroupApproximation.Algebra.AmenableLocallyFiniteByInt import GroupApproximation.Algebra.AmenableConstructions import GroupApproximation.Algebra.AmenableRat import GroupApproximation.Sofic.CliffordBSAmenable import GroupApproximation.Sofic.ProductMultiplicity import GroupApproximation.Sofic.ProductMultiplicityRank import GroupApproximation.Sofic.ContinuumMultiplicity import GroupApproximation.Sofic.ContinuumFamilyCriterion import GroupApproximation.Sofic.ContinuumFromNormalSubgroups import GroupApproximation.Sofic.OperatorMFPairAmplification import GroupApproximation.Sofic.OperatorMFLocalNormalization import GroupApproximation.Sofic.MarkedGroupTopology import GroupApproximation.Sofic.MarkedMFClosed import GroupApproximation.Criterion.FiniteQuotientBlindness import GroupApproximation.Criterion.LocalCriterion import GroupApproximation.Criterion.LocalizedApproximation import GroupApproximation.Criterion.SelectionOutput import GroupApproximation.Matching.Pinning import GroupApproximation.Matching.Refinement import GroupApproximation.Matching.Selection import GroupApproximation.Matching.MedianNormalization import GroupApproximation.Sofic.LEF import GroupApproximation.Sofic.FinitelyPresentedLEF import GroupApproximation.Sofic.ThompsonFObstruction import GroupApproximation.Sofic.AugmentationExtension import GroupApproximation.Criterion.Scheme import GroupApproximation.Criterion.Criterion import GroupApproximation.Matching.BlockEnumeration import GroupApproximation.Matching.BlockIndex import GroupApproximation.Matching.ComponentDivergence import GroupApproximation.Matching.GeneratorWords import GroupApproximation.Matching.BlockWordCrossing import GroupApproximation.Matching.BlockTransport import GroupApproximation.Matching.ComponentRefinement import GroupApproximation.Matching.DecompositionRefinement import GroupApproximation.Matching.FiniteGroupoidCounting import GroupApproximation.Matching.FiniteGroupoidPresentation import GroupApproximation.Matching.FinitePartialBijection import GroupApproximation.Matching.AsymptoticPartialBijection import GroupApproximation.Matching.AsymptoticPartialGroupoid import GroupApproximation.Matching.AsymptoticBlockArrow import GroupApproximation.Matching.FiniteGroupoidBisection import GroupApproximation.Matching.PartialBijectionSandwich import GroupApproximation.Matching.FinitePartialClusterGroupoid import GroupApproximation.Matching.PartialEquivarianceBoundary import GroupApproximation.Matching.PartialTaggedExpansion import GroupApproximation.Matching.ComponentInvolutionRepair import GroupApproximation.Matching.RepairedComponentBisection import GroupApproximation.Matching.BlockPartialBijection import GroupApproximation.Matching.EdgeEditing import GroupApproximation.Matching.GeneratorCrossing import GroupApproximation.Matching.ExternalCompressorCrossing import GroupApproximation.Matching.CompressionRefinement import GroupApproximation.Matching.FiniteMedian import GroupApproximation.Matching.NormalizedComponents import GroupApproximation.Matching.ComponentPinning import GroupApproximation.Matching.NormalizedVariation import GroupApproximation.Matching.InverseNormalization import GroupApproximation.Matching.GlobalVariation import GroupApproximation.Matching.SlowThreshold import GroupApproximation.Matching.FiniteMarkov import GroupApproximation.Matching.MatchingPreparation import GroupApproximation.Matching.MatchingSelection import GroupApproximation.Matching.EdgeWitnessDistance import GroupApproximation.Matching.EdgeWitnessRestriction import GroupApproximation.Matching.GeneratorGraphEditing import GroupApproximation.Matching.CompletionGraphEditing import GroupApproximation.Matching.SelectedGraphComparison import GroupApproximation.Matching.ConservativeMatching import GroupApproximation.Criterion.CriterionAssembly import GroupApproximation.Leavitt.Leavitt import GroupApproximation.Leavitt.FiniteModuleObstruction import GroupApproximation.Leavitt.UnitAdditiveSpan import GroupApproximation.Leavitt.FiniteDualOrbit import GroupApproximation.Leavitt.ElementaryWeylBridge import GroupApproximation.Leavitt.AtlasProperInfiniteCorner import GroupApproximation.Leavitt.TwoChildFiniteObstruction import GroupApproximation.Leavitt.FinitePairedQuotientObstruction import GroupApproximation.Leavitt.RobustPairedQuotientFloor import GroupApproximation.Leavitt.FiniteTreeCoupling import GroupApproximation.Leavitt.NonincidentFlagGram import GroupApproximation.Leavitt.RawWordReynoldsGap import GroupApproximation.Leavitt.S3S4BranchingBalance import GroupApproximation.Leavitt.AryCorner import GroupApproximation.Leavitt.FamilyRankFour import GroupApproximation.Leavitt.RawSwapCompressors import GroupApproximation.Leavitt.LeavittOverCommRing import GroupApproximation.Leavitt.IntegralGeneration import GroupApproximation.Leavitt.ElementaryPerfect import GroupApproximation.Leavitt.AryProfile import GroupApproximation.Leavitt.SelfSimilarityAlgebra import GroupApproximation.Leavitt.PlaneEmbedding import GroupApproximation.Leavitt.GeneralRankWords import GroupApproximation.Leavitt.Collision19243 import GroupApproximation.Leavitt.GeneralScheme import GroupApproximation.Leavitt.GeneralCornerTheorem import GroupApproximation.Sofic.LEFSofic import GroupApproximation.Sofic.NotVirtuallyLinear import GroupApproximation.Sofic.FreeGroupResiduallyFinite import GroupApproximation.Sofic.FreeProductSignReflection import GroupApproximation.Endpoint.QuotientNonclosure import GroupApproximation.Leavitt.AryLeavitt import GroupApproximation.Leavitt.AryCornerMatrix import GroupApproximation.Leavitt.AryEndpoints import GroupApproximation.Leavitt.UniversalLeavittOver import GroupApproximation.Leavitt.LeavittNormalForm import GroupApproximation.Leavitt.DiagonalClassGroup import GroupApproximation.KOne.GLIsElementary import GroupApproximation.Leavitt.LeavittDiagonalClass import GroupApproximation.Leavitt.BinaryLeavittDiagonal import GroupApproximation.KOne.StableUnitsGenerators import GroupApproximation.Leavitt.FamilyDiagonalClass import GroupApproximation.KOne.FieldMatrixReduction import GroupApproximation.Leavitt.LeavittDegreeZero import GroupApproximation.Leavitt.FamilyDescent import GroupApproximation.Leavitt.LeavittGradingSpans import GroupApproximation.Leavitt.LeavittBalancedUnits import GroupApproximation.Leavitt.LeavittWindowReduction import GroupApproximation.Leavitt.BinaryLeavittWindow import GroupApproximation.KOne.ScaledStreamRepresentation import GroupApproximation.KOne.VandermondeExtraction import GroupApproximation.KOne.GradedIndependence import GroupApproximation.KOne.BaseChangeIndependence import GroupApproximation.KOne.StableRankOne import GroupApproximation.KOne.BalancedStableRank import GroupApproximation.Leavitt.WhiteheadFlip import GroupApproximation.KOne.ResidualNormalForm import GroupApproximation.KOne.ResidualMoves import GroupApproximation.KOne.ResidualReduction import GroupApproximation.KOne.BalancedRegularity import GroupApproximation.KOne.WindowProductClosure import GroupApproximation.KOne.NilpotentTailKill import GroupApproximation.KOne.IncomparableUnipotents import GroupApproximation.KOne.ShapeCalculus import GroupApproximation.KOne.GradedComponents import GroupApproximation.KOne.PureTailNilpotency import GroupApproximation.Leavitt.RankNormalForm import GroupApproximation.KOne.DegreeShapeBridge import GroupApproximation.KOne.CylinderCornerRank import GroupApproximation.KOne.ZeroKOne import GroupApproximation.KOne.WidthTwoReduction import GroupApproximation.KOne.WindowNonnegReduction import GroupApproximation.KOne.OppositeTranspose import GroupApproximation.KOne.ThetaStable import GroupApproximation.KOne.WindowNonposReduction import GroupApproximation.KOne.CodeChangeInfrastructure import GroupApproximation.KOne.CodeChangeSwap import GroupApproximation.KOne.CodeChangeUnits import GroupApproximation.KOne.PencilCore import GroupApproximation.KOne.PencilForm import GroupApproximation.KOne.CodePairTransport import GroupApproximation.KOne.CodeScalarMoves import GroupApproximation.KOne.CodeRelativeFullness import GroupApproximation.KOne.CodeChangeGlue import GroupApproximation.KOne.AtomPeel import GroupApproximation.KOne.MixedCodeMoves import GroupApproximation.KOne.GLPairNormalization import GroupApproximation.KOne.PencilEntryArith import GroupApproximation.KOne.CompleteCodeSupply import GroupApproximation.KOne.GLVectorNormalization import GroupApproximation.KOne.RowClearMove import GroupApproximation.KOne.FullExtraction import GroupApproximation.KOne.MirrorExtraction import GroupApproximation.KOne.EntryStrip import GroupApproximation.KOne.EntrywiseKill import GroupApproximation.KOne.StackDichotomy import GroupApproximation.KOne.RefinedCodes import GroupApproximation.KOne.BalancedCodePencil import GroupApproximation.KOne.EntrywiseKillMirror import GroupApproximation.KOne.RefineStep import GroupApproximation.KOne.StrictNegativePencil import GroupApproximation.KOne.CodeShapeSupply import GroupApproximation.KOne.PencilReshape import GroupApproximation.KOne.RefineLoopDischarge import GroupApproximation.Leavitt.MatrixDiagonalization import GroupApproximation.Leavitt.LeavittSimplicity import GroupApproximation.Leavitt.LeavittRankEquivalence import GroupApproximation.Matching.FiniteGraph import GroupApproximation.Leavitt.LeavittCorner import GroupApproximation.Leavitt.LeavittMatrixCompression import GroupApproximation.Leavitt.DiagonalCornerCompression import GroupApproximation.Leavitt.DiagonalElementary import GroupApproximation.Leavitt.LeavittSelfSimilarity import GroupApproximation.Matching.Localization import GroupApproximation.Leavitt.MatrixSelfSimilarity import GroupApproximation.Matching.PermutationConservation import GroupApproximation.Sofic.Sofic import GroupApproximation.Sofic.SoficAmplification import GroupApproximation.Sofic.SoficUltraproduct import GroupApproximation.Sofic.HyperlinearMetric import GroupApproximation.Sofic.Hyperlinear import GroupApproximation.Sofic.HyperlinearAmplification import GroupApproximation.Quantum.FiniteMeasurement import GroupApproximation.Sofic.HyperlinearNonScalar import GroupApproximation.Sofic.HyperlinearScalar import GroupApproximation.Sofic.AntipodalTraceExtraction import GroupApproximation.Sofic.AntipodalRadicalCollision import GroupApproximation.Sofic.CliffordPhaseExtraction import GroupApproximation.Sofic.PhaseOrder import GroupApproximation.Sofic.MonomialModel import GroupApproximation.Sofic.PhasePropagation import GroupApproximation.Sofic.LeavittTraceFloor import GroupApproximation.Sofic.ScalarCocycle import GroupApproximation.Sofic.CharacterCount import GroupApproximation.Sofic.NoRounding import GroupApproximation.Sofic.RootableGroupFiniteImages import GroupApproximation.Sofic.PhaseCorrection import GroupApproximation.Sofic.ScalarClass import GroupApproximation.Sofic.RationalCharacter import GroupApproximation.Sofic.UntwistSeparation import GroupApproximation.Sofic.HeisenbergCentre import GroupApproximation.Sofic.HyperlinearReduction import GroupApproximation.Sofic.HyperlinearWeakBridge import GroupApproximation.Sofic.HyperlinearUltraproductBridge import GroupApproximation.Sofic.ImplementerCocycle import GroupApproximation.Sofic.CoordinateTransfer import GroupApproximation.Sofic.DivisibleInvisible import GroupApproximation.Sofic.HyperlinearUltraproduct import GroupApproximation.Sofic.NormTraceGap import GroupApproximation.Sofic.FaithfullyTracedCoordinateNoGo import GroupApproximation.Sofic.HilbertSchmidtAdjointGap import GroupApproximation.Sofic.PermutationAdjointGap import GroupApproximation.Sofic.AdjointOperatorNormRequirement import GroupApproximation.Sofic.KazhdanTransportFiniteDimensionalInputs import GroupApproximation.Sofic.WeakMFUltraproduct import GroupApproximation.Sofic.OpAlmostRepresentation import GroupApproximation.Sofic.NormMFResidualDetector import GroupApproximation.Sofic.MarkedCompressionData import GroupApproximation.Sofic.NormMFResidualFunctorial import GroupApproximation.Sofic.ApproxInvolutionCorner import GroupApproximation.Sofic.WeakMFTransfer import GroupApproximation.Sofic.WeakMFRegularTrace import GroupApproximation.Sofic.RegularCharacterGNS import GroupApproximation.Sofic.KazhdanCorner import GroupApproximation.Sofic.KazhdanCornerMatrices import GroupApproximation.Sofic.WeakMFVectorGNS import GroupApproximation.Sofic.KazhdanCornerModel import GroupApproximation.Sofic.KazhdanCornerDiagonal import GroupApproximation.Sofic.FreeLampReduction import GroupApproximation.Sofic.PushoutEmbedding import GroupApproximation.Sofic.SymmetricDoubleSubgroupReflection import GroupApproximation.Sofic.FreeLampDoubleEmbedding import GroupApproximation.Sofic.WeakMFNonsoficDouble import GroupApproximation.Sofic.SoficFiniteSemidirect import GroupApproximation.Sofic.SymmetricDoubleFlip import GroupApproximation.Sofic.LineDouble import GroupApproximation.Sofic.DoubleSoficTransfer import GroupApproximation.Sofic.MFNonsoficDoubleEndpoint import GroupApproximation.Sofic.FreeLampRigidity import GroupApproximation.Sofic.ProfiniteClosure import GroupApproximation.Sofic.CentralFreeLampCover import GroupApproximation.Sofic.CentralCoverInheritance import GroupApproximation.Sofic.CommutantPinning import GroupApproximation.Sofic.NearAction import GroupApproximation.Sofic.NearActionModel import GroupApproximation.Sofic.LevelShiftObstruction import GroupApproximation.Sofic.SoficPositiveControl import GroupApproximation.Sofic.SemanticPositiveControls import GroupApproximation.Sofic.SoficErrors import GroupApproximation.Sofic.Normalization import GroupApproximation.Sofic.InvolutiveCentralizerComponents import GroupApproximation.Leavitt.Whitehead import GroupApproximation.Covers.KazhdanCover import GroupApproximation.Covers.PresentedEnlargement import GroupApproximation.Covers.TableCover import GroupApproximation.Covers.HyperlinearTableCover import GroupApproximation.Leavitt.LeavittWords import GroupApproximation.Leavitt.PrefixCode import GroupApproximation.Leavitt.ElementaryGroup import GroupApproximation.Leavitt.ElementaryRoots import GroupApproximation.Leavitt.OuterRootLeavittRouting import GroupApproximation.Leavitt.ElementaryStabilization import GroupApproximation.Leavitt.RankFourCompressors import GroupApproximation.Leavitt.RankTwelveCompressor import GroupApproximation.Leavitt.ElementaryNormalGeneration import GroupApproximation.Leavitt.RankTwelvePropertyT import GroupApproximation.Leavitt.UniversalLeavitt import GroupApproximation.Leavitt.UniversalRankFour import GroupApproximation.Leavitt.UniversalPropertyT import GroupApproximation.Leavitt.ZeroRangeObstruction import GroupApproximation.PropertyTT.PaperStatements import GroupApproximation.PropertyTT.NonsoficCorollary import GroupApproximation.Leavitt.UniversalCompressionSetup import GroupApproximation.Leavitt.ThompsonV import GroupApproximation.Leavitt.ThompsonVEmbedding import GroupApproximation.Leavitt.FamilyVEmbedding import GroupApproximation.Leavitt.ThompsonVWitness import GroupApproximation.Leavitt.ThompsonWitness import GroupApproximation.Matching.MatchedComponents import GroupApproximation.Sofic.SoficTransfer import GroupApproximation.Sofic.SoficDirectedUnion import GroupApproximation.Sofic.CliffordLampPermanence import GroupApproximation.Sofic.IntegralLinearResiduallyFinite import GroupApproximation.Sofic.SoficFiniteKernelSemidirect import GroupApproximation.Sofic.SoficInvariantFiniteKernel import GroupApproximation.Sofic.FiniteOrbitInvariantKernel import GroupApproximation.Sofic.MappingTelescopeFiniteOrbits import GroupApproximation.Sofic.SoficIntegerExtension import GroupApproximation.Sofic.SoficTelescope import GroupApproximation.Monsters.ExplicitIntegralLinearModel import GroupApproximation.Endpoint.NonMFImpact import GroupApproximation.Sofic.HyperlinearResidualDetector import GroupApproximation.Sofic.FiniteLinearHammingGap import GroupApproximation.Sofic.RelativeImplementerCentralizer import GroupApproximation.Sofic.FiniteResidualKernel import GroupApproximation.Sofic.InternalRadicalGap import GroupApproximation.Sofic.AuxiliaryClassSeparation import GroupApproximation.Sofic.StarGaussian import GroupApproximation.Sofic.FermionicOptimality import GroupApproximation.Endpoint.MainResults import GroupApproximation.Endpoint.SimultaneousStability import GroupApproximation.Endpoint.StructuralProfile import GroupApproximation.Leavitt.UnitsGLProfile import GroupApproximation.KOne.AllRanksElementary import GroupApproximation.Kazhdan.KazhdanTextbook import GroupApproximation.Monsters.Terminality import GroupApproximation.Monsters.TwoConjugacyClasses import GroupApproximation.Monsters.VerbalCompleteness import GroupApproximation.Monsters.Protection import GroupApproximation.Monsters.UniversalMFEventHorizon import GroupApproximation.Monsters.UniversalFinitelyPresentedTorsionFreeGroup import GroupApproximation.Monsters.TorsionFreeConjugacyExtension import GroupApproximation.Monsters.HitchhikerPayload import GroupApproximation.Endpoint.Audit import GroupApproximation.Endpoint.Public import GroupApproximation.Endpoint.ManuscriptStatements import GroupApproximation.Sofic.SoficSequential import GroupApproximation.KOne.WhiteheadQuotient import GroupApproximation.KOne.ClassicalKOne import GroupApproximation.KOne.FactorizationCertificate import GroupApproximation.KOne.PaperStatements import GroupApproximation.Leavitt.FiniteTypeCountable import GroupApproximation.Leavitt.FiniteOutcomeCoarsening import GroupApproximation.Leavitt.FiniteNoSignalingPairingBox import GroupApproximation.Leavitt.FiniteBinaryFiberDecoder import GroupApproximation.Leavitt.PauliCarrierBinaryGap import GroupApproximation.Leavitt.ShiftEndomorphism import GroupApproximation.Sofic.LocalCentralQuotientLifting import GroupApproximation.Steinberg.KervaireSteinberg import GroupApproximation.Criterion.FiniteDimensionalKill import GroupApproximation.Sofic.KazhdanCliffordEpsilon import GroupApproximation.Algebra.ZariskiClosedSubgroup import GroupApproximation.Algebra.ZariskiDescendingChain import GroupApproximation.Algebra.DyadicRationals import GroupApproximation.Algebra.DiagonalCosetAction import GroupApproximation.Algebra.WordMetric import GroupApproximation.Monsters.LiteralDyadicCalibration import GroupApproximation.Sofic.SoficByAmenablePermanence import GroupApproximation.Analysis.PropertyTNonamenable import GroupApproximation.Analysis.ResiduallyFiniteDimensional import GroupApproximation.Analysis.MaximalCStarParagraphEndpoint import GroupApproximation.Sofic.ManuscriptCentralSignCriterion import GroupApproximation.Sofic.CollapseUniverseScopeDefs import GroupApproximation.Sofic.CollapseUniverseScope import GroupApproximation.Sofic.CollapseProfileBound import GroupApproximation.Analysis.CStarTensorProductAdjointable import GroupApproximation.Analysis.ExactnessPermanence import GroupApproximation.Computability.SemigroupWordProblemRewriting import GroupApproximation.Monsters.FournierFacioRealization import GroupApproximation.Monsters.P13SpectralGap import GroupApproximation.Sofic.CollapseProfileBoundNumeric import GroupApproximation.Sofic.CollapseTransportDiagonalization import GroupApproximation.Sofic.CollapseTransportDiagonalizationCommutant import GroupApproximation.Sofic.CollapseWordMetric import GroupApproximation.Sofic.GraphCliffordLamp import GroupApproximation.Sofic.LiteralAffineCosetTransitivity import GroupApproximation.Sofic.LiteralBlockGeometry import GroupApproximation.Sofic.LiteralBlockNormalForm import GroupApproximation.Sofic.LiteralLampKernelSplit import GroupApproximation.Sofic.LiteralTelescopeCoreLEF import GroupApproximation.Sofic.MatricialStabilityInstances import GroupApproximation.Sofic.SimpleSoficEnvelope import GroupApproximation.Sofic.SoficEnvelopeExistence import GroupApproximation.Sofic.UltraproductIntertwinerTransport import GroupApproximation.Sofic.UltraproductScaledTransport import GroupApproximation.Sofic.MultiMoverUniversalUpgrade import GroupApproximation.Sofic.AscendingHNNSeparableCosetAction import GroupApproximation.Sofic.SimpleFullMFRadical import GroupApproximation.Computability.RewriteDeterminism import GroupApproximation.Analysis.NuclearityAmenability import GroupApproximation.Computability.RewriteSimulation import GroupApproximation.Monsters.NeumannContinuum import GroupApproximation.Computability.UnaryCounterSimulation import GroupApproximation.Computability.PostMachine import GroupApproximation.Computability.PostMachineHalting import GroupApproximation.Computability.HaltingReduction import GroupApproximation.Computability.RewriteSimulationOn import GroupApproximation.Sofic.SimpleLampNormalGeneration import GroupApproximation.Sofic.UniversalVisibleQuotient import GroupApproximation.Sofic.SimpleFactorRecovery import GroupApproximation.Sofic.RadicalFiniteIndexTransfer import GroupApproximation.Sofic.KazhdanCliffordConstruction import GroupApproximation.Sofic.LiteralBaseP13PropertyTBridge import GroupApproximation.Sofic.LiteralMFQuotientControls import GroupApproximation.Sofic.LiteralNonMFConsequences import GroupApproximation.Sofic.LiteralNonMFPresentation import GroupApproximation.Sofic.LiteralUniformObstruction import GroupApproximation.Sofic.RelatorDefectBudget import GroupApproximation.Sofic.LiteralRelatorObstruction import GroupApproximation.Sofic.ExactCoronaNegativeCorner import GroupApproximation.Sofic.LiteralTheoremAPackage import GroupApproximation.Sofic.ManuscriptExactWrappers import GroupApproximation.Sofic.ManuscriptSubgroupSpecializations import GroupApproximation.Sofic.TorsionFreeFiniteNormalLimit -- Modules that until now compiled only in isolation. Outside the root import -- closure nothing in CI ever built them, so their proofs went unverified in every -- run that mattered; `scripts/check.py --list-orphans` is the scan. The rest of -- the orphan set stays out on purpose: some of it is work other sessions have in -- flight, and some has gone stale against renames upstream of it. Wiring either -- kind in here breaks the root build for everyone instead of getting it verified. -- -- The four below are in because `Sofic/LiteralSoficAssembly.lean` is now cited by -- Theorem `thm:Esofic` in the manuscript, and `check_non_mf_refs.py` rejects a -- badge on an unbuilt module in as many words: outside the closure `lake build` -- never compiles it, so the badge certifies nothing. The other three are that -- module's own dependencies, listed rather than left implicit so that dropping -- one is a visible edit. Every one of the four is tracked and fully proved. import GroupApproximation.Sofic.BlockCliffordTowerSofic import GroupApproximation.Sofic.LiteralSoficConsequences import GroupApproximation.Sofic.LiteralSoficEndpoint import GroupApproximation.Sofic.LiteralVerticalBridge -- The modules below were kept out under the rule above, on the presumption that -- they did not compile. Each has now been compiled against the warm cache with -- the pinned toolchain -- exit 0, no messages, olean emitted -- so the reason for -- keeping them out no longer applies, and leaving them out would keep CI blind to -- proofs that are in fact finished. Several needed only a one-line repair to get -- there: a missing `Mathlib.GroupTheory.FreeGroup.Reduce` import, a universe -- declared `Type*` against a `Type` dependency, and two files that ended in -- leaked tool markup. -- -- The remaining orphans stay out for the original reason: they are either in -- flight in another session or genuinely broken. import GroupApproximation.Computability.FreeByRetraction import GroupApproximation.Computability.HNNPresentedForward import GroupApproximation.Computability.PresentedGroupBasisChange import GroupApproximation.Computability.RabinBrittonFreeness import GroupApproximation.Computability.RabinConstruction import GroupApproximation.Computability.RabinConstructionMF import GroupApproximation.Computability.RabinConstructionSource import GroupApproximation.Computability.RabinFreeLetterOrder import GroupApproximation.Computability.SemigroupWordProblemMachine import GroupApproximation.Sofic.LiteralSoficSeparation import GroupApproximation.Sofic.SimpleNotLEF import GroupApproximation.Sofic.RationalEnvelope import GroupApproximation.Sofic.RepresentationCategoryTwins -- Restored 2026-08-16: a root-file sweep dropped these while wiring in others. -- Each compiles and each was in the closure before, so the removal silently -- un-verified them. import GroupApproximation.Computability.ListBlankCanonical import GroupApproximation.Computability.PostMachineTM0 import GroupApproximation.Computability.PostMachineTM0Canonical import GroupApproximation.Computability.TM0WordProblem import GroupApproximation.Sofic.ActionFormMoverEstimate import GroupApproximation.Sofic.FullRadicalClosureProperties import GroupApproximation.Sofic.WreathFinitePresentationObstruction import GroupApproximation.Sofic.TelescopeLimitUnion import GroupApproximation.Sofic.TelescopeRadicalInduction import GroupApproximation.Sofic.BlockCliffordIndex import GroupApproximation.Sofic.LiteralCosetBraid import GroupApproximation.Computability.FreeGroupSquaring import GroupApproximation.Computability.SemigroupWordProblemSimulation import GroupApproximation.Computability.SemigroupWordProblemPresentation import GroupApproximation.Computability.SemigroupWordProblem -- Added by the 1:1 audit pass: modules that were outside the import closure, -- so `lake build` never compiled them and no audit ever saw them. Appended, -- never regenerated -- a regenerated block has twice silently dropped modules. import GroupApproximation.Analysis.FiniteCStarMurrayVonNeumann import GroupApproximation.Analysis.MaximalCStarLiteralBase import GroupApproximation.Analysis.MaximalGroupCStarUniqueness import GroupApproximation.Analysis.PropertyAExtension import GroupApproximation.Analysis.ExactnessGroupSideEndpoint import GroupApproximation.Analysis.PropertyALocality import GroupApproximation.Analysis.PropertyATelescope import GroupApproximation.Analysis.PropertyAFiniteKernel import GroupApproximation.Analysis.CStarTensorProductSeminorm import GroupApproximation.Analysis.CStarTensorProductSpatial import GroupApproximation.Analysis.CStarTensorProductConcrete import GroupApproximation.Analysis.CStarTensorProductAlgebra import GroupApproximation.Analysis.CStarStateSeparation import GroupApproximation.Analysis.CStarStateGNS import GroupApproximation.Analysis.CStarStatePullback import GroupApproximation.Analysis.CStarMinTensorNorm import GroupApproximation.Analysis.CStarSliceBound import GroupApproximation.Analysis.CStarSliceCompletion import GroupApproximation.Analysis.CStarSliceLeft import GroupApproximation.Analysis.CStarExactnessSliceReduction import GroupApproximation.Analysis.CStarSliceIdeal import GroupApproximation.Analysis.CStarMaxTensorNorm import GroupApproximation.Analysis.CStarTensorComparison import GroupApproximation.Analysis.CStarNuclearity import GroupApproximation.Analysis.CStarTensorComparisonRange import GroupApproximation.Analysis.CStarMinTensorFunctorial import GroupApproximation.Analysis.CStarMinTensorQuotient import GroupApproximation.Analysis.CStarNonUnitalState import GroupApproximation.Analysis.CStarCompletelyPositiveForm import GroupApproximation.Analysis.CStarCompletelyPositiveStar import GroupApproximation.Analysis.CStarStinespringForm import GroupApproximation.Analysis.CStarStinespringSpace import GroupApproximation.Analysis.CStarStinespringBound import GroupApproximation.Analysis.CStarStinespringAct import GroupApproximation.Analysis.CStarStinespringDefect import GroupApproximation.Analysis.CStarStinespringMul import GroupApproximation.Analysis.CStarStinespringRep import GroupApproximation.Analysis.CStarStinespringLinear import GroupApproximation.Analysis.CStarStinespringDilation import GroupApproximation.Analysis.CStarStinespringHom import GroupApproximation.Analysis.LanceReiterMean import GroupApproximation.Analysis.CStarIdealQuotient import GroupApproximation.Analysis.CStarQuotientIdentity import GroupApproximation.Analysis.CStarIdealApproximateUnit import GroupApproximation.Analysis.CStarProductCorona import GroupApproximation.Analysis.CStarTensorProduct import GroupApproximation.Algebra.ZariskiEnvelopeEndpoint import GroupApproximation.Criterion.ClosedEnvelopeCompressionCore import GroupApproximation.Monsters.RealizationEmbedding import GroupApproximation.Monsters.FournierFacioUniversalRealization import GroupApproximation.Monsters.P13InvariantProjection import GroupApproximation.Sofic.CompressionUniverseTransfer import GroupApproximation.Sofic.TransportVariantsAnyUniverse import GroupApproximation.Sofic.ConjugationDatumAnyUniverse import GroupApproximation.Sofic.FiniteNormalAnyUniverse import GroupApproximation.Sofic.SoundIterateInstances import GroupApproximation.Sofic.ContinuumMultiplicityCore import GroupApproximation.Sofic.PrintedPreliminaryEstimates import GroupApproximation.Sofic.PrintedCentralSignCriterion import GroupApproximation.Sofic.PrintedNegativeCornerKill import GroupApproximation.Sofic.PrintedReverseTransportRoute import GroupApproximation.Sofic.LiteralSignFreeRadicalReduction import GroupApproximation.Sofic.SoficEnvelopeSimplicity import GroupApproximation.Sofic.BoundedConjProductAlgebra import GroupApproximation.Sofic.SoficEnvelopeWitness import GroupApproximation.Sofic.CollapsePrintedProfile import GroupApproximation.Sofic.CliffordBSSixRelator import GroupApproximation.Sofic.CliffordBSPrintedRoute import GroupApproximation.Sofic.WreathWitnessGeneric import GroupApproximation.Sofic.WreathWitnessW3 import GroupApproximation.Sofic.FiveConditionInsufficiency import GroupApproximation.Sofic.Type0Corollaries import GroupApproximation.Sofic.WreathWitnessSignFree import GroupApproximation.Sofic.WeightedUltraproductModelConstruction import GroupApproximation.Sofic.CollapseJointCornerRefinement import GroupApproximation.Sofic.AmalgamQuestionEndpoint import GroupApproximation.Sofic.LiteralBlockCliffordBridge import GroupApproximation.Sofic.LiteralLampKernelAmalgam import GroupApproximation.Sofic.DirectSumAmplification import GroupApproximation.Sofic.CornerDilutionInvariance import GroupApproximation.Sofic.LiteralBaseRotationMatrix import GroupApproximation.Sofic.CollapseScaledStepSix import GroupApproximation.Sofic.CollapseJointCorner import GroupApproximation.Sofic.CollapseWordMetricBridge import GroupApproximation.Analysis.MFStablyFinite import GroupApproximation.Analysis.PreliminaryInequalitiesPrinted import GroupApproximation.Analysis.StrictCompressionFromPrinted import GroupApproximation.Criterion.StandardRepCommutant import GroupApproximation.Monsters.NeumannNormalSubgroups import GroupApproximation.Sofic.IntrinsicCompressionFiniteStage import GroupApproximation.Computability.UniversalMachineInit import GroupApproximation.Sofic.CollapseTransportEndpoint import GroupApproximation.Sofic.CollapsePrintedDiagonalization import GroupApproximation.Sofic.CollapsePrintedCorollary import GroupApproximation.Computability.MachineRestrict import GroupApproximation.Sofic.CliffordLampGraphLocalFiniteness import GroupApproximation.Sofic.CliffordLampGraphFreeSubgroup import GroupApproximation.Sofic.CliffordBSAmenableMF import GroupApproximation.Sofic.CliffordQuotientMFUnconditional import GroupApproximation.Sofic.DefectActionAnyUniverse import GroupApproximation.Sofic.DefectRadicalAnyUniverse import GroupApproximation.Sofic.InvolutionsAnyBase import GroupApproximation.Sofic.NormalKazhdanAnyUniverse import GroupApproximation.Sofic.TensorPowerAnyUniverse import GroupApproximation.Computability.FiniteMachineWordProblem import GroupApproximation.Computability.MarkovPost import GroupApproximation.Computability.BooneGroupFreeBasis import GroupApproximation.Computability.BooneGroupModularMachine import GroupApproximation.Computability.BooneGroupBase import GroupApproximation.Computability.BooneGroupPresentation import GroupApproximation.Computability.BooneGroupTower import GroupApproximation.Computability.BooneGroupGoodness import GroupApproximation.Computability.BooneBaseWords import GroupApproximation.Computability.BooneTowerPresentation import GroupApproximation.Computability.QuadMachine import GroupApproximation.Computability.QuadMachineTM0 import GroupApproximation.Computability.ModularMachineUndecidable import GroupApproximation.Computability.ComputableConfigReduction import GroupApproximation.Computability.BinaryDigitPrimrec import GroupApproximation.Computability.TrNatRecurrence import GroupApproximation.Computability.IndexMapComputable import GroupApproximation.Computability.BooneWordProblem import GroupApproximation.Computability.BooneGroupMachineIndex import GroupApproximation.Computability.UniversalMachineUndecidable import GroupApproximation.Computability.AdianRabinWordProblem import GroupApproximation.Algebra.HNNFinitePresentation import GroupApproximation.Algebra.HNNPresentation import GroupApproximation.Algebra.HNNPresentationQuotient import GroupApproximation.Algebra.RabinVariantPresentation import GroupApproximation.Computability.RabinVariantMF import GroupApproximation.Algebra.RabinVariantTower import GroupApproximation.Algebra.HNNRetraction import GroupApproximation.Algebra.HNNTrivialAssociated import GroupApproximation.Algebra.PresentedGroupRelabel import GroupApproximation.Algebra.HNNCongr import GroupApproximation.Algebra.FreeProductOrder import GroupApproximation.Computability.BooneGroupFinitePresentation import GroupApproximation.Computability.NovikovBoone import GroupApproximation.Computability.BooneGroupCode import GroupApproximation.Computability.UniformWordProblemUndecidable import GroupApproximation.Computability.CodedWordTriviality import GroupApproximation.Computability.FreeGroupCheckerPrimrec import GroupApproximation.Computability.FreeGroupDeletion import GroupApproximation.Computability.FreeGroupDeletionPrimrec import GroupApproximation.Computability.FreeGroupRedNil import GroupApproximation.Computability.ModularMachineConfigHalting import GroupApproximation.Computability.BooneWords import GroupApproximation.Computability.BooneWordMapPrimrec import GroupApproximation.Computability.BooneWordAgreement import GroupApproximation.Computability.BooneWordProblemUndecidable import GroupApproximation.Analysis.PrintedLiftingSteps import GroupApproximation.Analysis.FiniteExceptionalPatch import GroupApproximation.Kazhdan.PrintedComplexificationBridge import GroupApproximation.Sofic.CentralSignAnyUniverse import GroupApproximation.Analysis.OmegaHilbertComplete import GroupApproximation.Analysis.RankFrobeniusBound import GroupApproximation.Sofic.RealizationFromUniversalGroup import GroupApproximation.Analysis.PrintedReverseTransport import GroupApproximation.Algebra.AlternatingBoundedNormalGeneration import GroupApproximation.Algebra.AlternatingDoubledTransport import GroupApproximation.Analysis.CollapseCocycleAnalytic import GroupApproximation.Analysis.MaximalCStarAnyUniverse import GroupApproximation.Analysis.NormalKazhdanUltraproduct import GroupApproximation.Analysis.OmegaConjugationOperators import GroupApproximation.Analysis.OmegaCommutatorFixes import GroupApproximation.Analysis.RankNormalizedHilbertization import GroupApproximation.Analysis.RankNormalizedLambda import GroupApproximation.Analysis.CollapseDisplacementIdeal import GroupApproximation.Analysis.CollapseTransportEndpoint import GroupApproximation.Analysis.CollapseCoronaIsometry import GroupApproximation.Analysis.CollapseDelormeCorona import GroupApproximation.Analysis.CollapseRouteJoin import GroupApproximation.Analysis.CollapseCompressionBundle import GroupApproximation.Analysis.CollapsePrintedContradiction import GroupApproximation.Analysis.CollapsePrintedProjectionCollapse import GroupApproximation.Analysis.PrintedFiniteException import GroupApproximation.Analysis.CollapseDiscardCoordinates import GroupApproximation.Analysis.CollapseLambdaCocycle import GroupApproximation.Analysis.CollapseInvariantSubspace import GroupApproximation.Analysis.CollapseKqTransport import GroupApproximation.Analysis.CollapseProjectionLift import GroupApproximation.Monsters.NeumannTwoGenerator import GroupApproximation.Sofic.CollapseRankWeightTransport import GroupApproximation.Sofic.FinitePacketCovariance import GroupApproximation.Sofic.FinitePacketDelormeCenter import GroupApproximation.Sofic.FiniteGroupUlamStep import GroupApproximation.Sofic.FiniteGroupUlamIteration import GroupApproximation.Sofic.FiniteGroupCoronaExactification import GroupApproximation.Sofic.FinitePacketRankWeight import GroupApproximation.Sofic.StarTranspositionRankMass import GroupApproximation.Sofic.FinitePacketCollapseCore import GroupApproximation.Endpoint.FinitePacketCollapseAudit import GroupApproximation.Sofic.StableLetterLEFRoute import GroupApproximation.Manuscript.NonMF.ClosedRows import GroupApproximation.Analysis.MatrixReindexHilbertSchmidt import GroupApproximation.Analysis.CollapseDelormeEndpoint import GroupApproximation.Analysis.ProperIsometryStrictOrder import GroupApproximation.Analysis.OmegaDefectExtraction import GroupApproximation.Analysis.UltraproductRigidityRoute import GroupApproximation.Manuscript.NonMF.QuestionAtoms import GroupApproximation.Sofic.LiteralTraceConsequence import GroupApproximation.Analysis.ShulmanTraceClasses import GroupApproximation.Sofic.ShulmanMFTraceBridge import GroupApproximation.Analysis.MaximalGroupCStarTrace import GroupApproximation.Analysis.MaximalGroupCStarSubgroupReflection import GroupApproximation.Analysis.ShulmanTraceNorms import GroupApproximation.Analysis.TracialMatrixUltraproduct import GroupApproximation.Analysis.ShulmanTraceFactorization import GroupApproximation.Analysis.ShulmanTraceFromRepresentation import GroupApproximation.Analysis.TracialUltraproductCStar import GroupApproximation.Analysis.UltrafilterDiagonalExtraction import GroupApproximation.Analysis.ShulmanTracePositiveControls import GroupApproximation.Analysis.HilbertSchmidtApproximateUnit import GroupApproximation.Sofic.MFTraceCoronaBridge import GroupApproximation.Sofic.SoficPermutationTrace import GroupApproximation.Analysis.TracialQuotientCStar import GroupApproximation.Analysis.SoficHyperlinearTrace import GroupApproximation.Analysis.TracialQuotientCStarIdentity import GroupApproximation.Analysis.SoficHyperlinearBridge import GroupApproximation.Analysis.PrintedUltrafilterHyperlinearTrace import GroupApproximation.Sofic.TraceSeparationEndpoint -- Modules that stood outside this root's import closure and were therefore -- never compiled by an ordinary `lake build`: `scripts/check.py --list-orphans` -- named twenty-eight of them, and ten did not elaborate at all. They carry the -- literal-route transport, the coordinate Hilbert ultraproduct `H_ω`, the -- C*-completion chain, general polar lifting, stably finite amplification and -- the unconditional simple sofic envelope -- the very files the manuscript -- correspondence needs -- so an unbuilt module here reads as coverage that does -- not exist. They are wired in below. import GroupApproximation.Algebra.AlternatingPairGeneration import GroupApproximation.Algebra.GroupRingStar import GroupApproximation.Algebra.PermutationTwoInvolutions import GroupApproximation.Algebra.InvolutionBlocks import GroupApproximation.Algebra.InvolutionBlockSplit import GroupApproximation.Algebra.InvolutionBlockAssembly import GroupApproximation.Analysis.CStarCompletion import GroupApproximation.Analysis.CStarCompletionCoe import GroupApproximation.Analysis.CStarCompletionHom import GroupApproximation.Analysis.CStarSeminormQuotient import GroupApproximation.Analysis.CStarNormBundled import GroupApproximation.Analysis.CStarQuotientHom import GroupApproximation.Analysis.CStarNormFromRepresentation import GroupApproximation.Analysis.CStarSeminormCompletion import GroupApproximation.Analysis.MaximalCStarAllUniverses import GroupApproximation.Analysis.MaximalCStarPrintedCompletion import GroupApproximation.Analysis.CollapseUltraproductRepresentation import GroupApproximation.Analysis.OmegaActionLinear import GroupApproximation.Analysis.OmegaIsometryRepresentation import GroupApproximation.Analysis.OmegaConjQCompatibility import GroupApproximation.Analysis.CollapseKqAlmostRep import GroupApproximation.Analysis.OmegaFiniteComparison import GroupApproximation.Analysis.OmegaFixRange import GroupApproximation.Analysis.PolarLiftingGeneralCStar import GroupApproximation.Analysis.FiniteBlockCoronaHilbert import GroupApproximation.Analysis.PolarLiftingPrintedSequence import GroupApproximation.Analysis.MFAlgebraDimensionNormalization import GroupApproximation.Analysis.MatrixCoronaAmplificationEmbedding import GroupApproximation.Analysis.CompatibleMatrixCoronaAmplification import GroupApproximation.Analysis.NormCoronaAsymptoticLiftModel import GroupApproximation.Analysis.NormCoronaAsymptoticLiftCore import GroupApproximation.Analysis.NormCoronaAsymptoticLift import GroupApproximation.Analysis.PolarLiftingHypothesisFree import GroupApproximation.Analysis.StablyFiniteAmplification import GroupApproximation.Analysis.MatrixCoronaDedekindFinite import GroupApproximation.Analysis.MFAlgebraMatrixAmplification import GroupApproximation.Analysis.ReducedProductMFPermanence import GroupApproximation.Analysis.MFAlgebraAmalgamGenerated import GroupApproximation.Analysis.MFAlgebraAmalgamCriterion import GroupApproximation.Analysis.CoronaProjectionOrder import GroupApproximation.Analysis.VectorHilbertUltraproduct import GroupApproximation.Analysis.VectorHilbertComplete import GroupApproximation.Analysis.VectorOmegaAction import GroupApproximation.Analysis.VectorOmegaKazhdanGap import GroupApproximation.Analysis.FilterMatrixCStarCorona import GroupApproximation.Analysis.VectorOmegaCoronaAction import GroupApproximation.Analysis.CoronaProjectionLifting import GroupApproximation.Analysis.UnitaryAverageFixedVector import GroupApproximation.Analysis.OmegaCoronaKazhdanProjection import GroupApproximation.Analysis.PrintedDiagonalSubsequence import GroupApproximation.Analysis.PrintedCornerCompression import GroupApproximation.Analysis.PrintedCornerAssembly import GroupApproximation.Analysis.FiniteDimensionalOperatorFinite import GroupApproximation.Analysis.PrintedCornerRelabelling import GroupApproximation.Analysis.PolarLiftingMatrixBlocks import GroupApproximation.Sofic.OmegaRouteManuscriptTransport import GroupApproximation.Sofic.LiteralProductMultiplicity import GroupApproximation.Sofic.SimpleSoficEnvelopeAnyUniverse import GroupApproximation.Sofic.PrintedTransportOpening import GroupApproximation.Sofic.KazhdanTransportFailureExtraction import GroupApproximation.Monsters.NeumannSimpleSocle import GroupApproximation.Sofic.TransportShapeBridges import GroupApproximation.Sofic.GeneralModelKazhdanTransport import GroupApproximation.Sofic.LiteralRouteTransport import GroupApproximation.Sofic.SimpleSoficEnvelopeUnconditional import GroupApproximation.Sofic.ConsistencyDistance import GroupApproximation.Analysis.CStarTakesakiCoefficient import GroupApproximation.Analysis.LancePositiveDefinite import GroupApproximation.Analysis.LanceReduction import GroupApproximation.Analysis.LanceMultiplicativeDomain import GroupApproximation.Analysis.CStarTakesakiDense import GroupApproximation.Analysis.CStarTakesakiMinLe import GroupApproximation.Analysis.CStarTakesakiCyclic import GroupApproximation.Analysis.CStarTakesakiIdentification import GroupApproximation.Analysis.TracialStandardFormCommutation import GroupApproximation.Analysis.TracialConjugationExists import GroupApproximation.Analysis.QuasidiagonalCompression import GroupApproximation.Analysis.UniformRoeAlgebra import GroupApproximation.Analysis.AmenableMFInput import GroupApproximation.Sofic.CliffordAsideInert import GroupApproximation.Sofic.ContainsSquareWitness import GroupApproximation.Analysis.CStarMinTensorInjective import GroupApproximation.Analysis.CStarExactComplex import GroupApproximation.Algebra.WordMetricBall import GroupApproximation.Analysis.CoarseCompression import GroupApproximation.Analysis.SchoenbergKernel import GroupApproximation.Analysis.GuentnerKaminker import GroupApproximation.Analysis.PropertyASquareWitness import GroupApproximation.Manuscript.NonMF.QuestionOneOpenness import GroupApproximation.Manuscript.NonMF.QuestionTwoRemainder import GroupApproximation.Sofic.FournierFacioUniversalGroup import GroupApproximation.Sofic.GreendlingerInduction import GroupApproximation.Sofic.GreendlingerIsoperimetric import GroupApproximation.Sofic.GreendlingerMinimal import GroupApproximation.Sofic.GreendlingerMirror import GroupApproximation.Sofic.GreendlingerOverlap import GroupApproximation.Sofic.GreendlingerRegime import GroupApproximation.Sofic.GreendlingerSlide import GroupApproximation.Sofic.GreendlingerWeight import GroupApproximation.Sofic.SmallCancellationKazhdanEnvelope import GroupApproximation.Analysis.OmegaUnitaryRepExists import GroupApproximation.Sofic.HSDistVanishingWitness import GroupApproximation.Analysis.L2KernelOperator import GroupApproximation.Computability.AdianRabinGeneral import GroupApproximation.Analysis.CStarChoiMap import GroupApproximation.Algebra.CoprodIPresentation import GroupApproximation.Algebra.FreeProductCyclicWord import GroupApproximation.Algebra.FreeProductUnionNorm import GroupApproximation.Algebra.HyperbolicGroup import GroupApproximation.Algebra.HyperbolicInteger import GroupApproximation.Algebra.HyperbolicQuasiIsometry import GroupApproximation.Algebra.HyperbolicSlimFourPoint import GroupApproximation.Algebra.HyperbolicSlimTriangles import GroupApproximation.Algebra.TorsionFreeQuotient import GroupApproximation.Algebra.TorsionFreeRadical import GroupApproximation.Algebra.TorsionFreeRadicalTower import GroupApproximation.Algebra.WordMetricComparison import GroupApproximation.Analysis.CStarCorestrictCP import GroupApproximation.Analysis.CStarFormCompletelyPositive import GroupApproximation.Analysis.CStarUnitalCPContractive import GroupApproximation.Analysis.CompressionTraceFolner import GroupApproximation.Analysis.CompressionTraceLocallyFinite import GroupApproximation.Analysis.CompressionTraceModel import GroupApproximation.Analysis.CompressionTraceRigidity import GroupApproximation.Analysis.GaussianRoeOperator import GroupApproximation.Analysis.GuentnerKaminkerEndpoint import GroupApproximation.Analysis.MFTracePullback import GroupApproximation.Analysis.NuclearApproximationEstimate import GroupApproximation.Analysis.QuasidiagonalTrace import GroupApproximation.Analysis.ReducedGroupCStarSpan import GroupApproximation.Analysis.RoeSquareRoot import GroupApproximation.Analysis.TikuisisWhiteWinter import GroupApproximation.Analysis.TikuisisWhiteWinterUnconditional import GroupApproximation.Analysis.UCPContractiveMatrix import GroupApproximation.Computability.OperatorMFMarkovData import GroupApproximation.Computability.SoficMarkov import GroupApproximation.Higman.Benign import GroupApproximation.Higman.BenignClosure import GroupApproximation.Kazhdan.TorsionFreeHyperbolicKazhdan import GroupApproximation.Monsters.ChiodoFreeProductAbsorber import GroupApproximation.Monsters.ChiodoTorsionFreeAbsorber import GroupApproximation.Monsters.RecursiveCodeAbsorber import GroupApproximation.Sofic.ChiodoBelegradekTheorem import GroupApproximation.Sofic.ChiodoUniversalHost import GroupApproximation.Sofic.ExplicitSuitableDefect import GroupApproximation.Sofic.GreendlingerTwoPieceRegime import GroupApproximation.Sofic.HullPrescribedSaturation import GroupApproximation.Sofic.HullSuitableDefectSubgroup import GroupApproximation.Sofic.FournierFacioHullBridge import GroupApproximation.Sofic.InfranormalCompressionPair import GroupApproximation.Sofic.KunThomDoubleWitness import GroupApproximation.Sofic.TikuisisWhiteWinterSharpness import GroupApproximation.Sofic.TikuisisWhiteWinterSites import GroupApproximation.Algebra.CoprodIFinitePresentation import GroupApproximation.Algebra.PushoutIFinitePresentation import GroupApproximation.Analysis.LanceAmenableOverlap import GroupApproximation.Analysis.LanceFolnerCPAP import GroupApproximation.Analysis.LanceFolnerMaps import GroupApproximation.Analysis.LanceNuclearAmenable import GroupApproximation.Analysis.TikuisisWhiteWinterAmenableClass import GroupApproximation.Kazhdan.SharpExistenceRoutes import GroupApproximation.Algebra.FreeProductConjugacy import GroupApproximation.Analysis.CStarOrderZero import GroupApproximation.Higman.RopeTrick import GroupApproximation.Sofic.GreendlingerThreeFactor import GroupApproximation.Sofic.HullSuitabilityGeometry import GroupApproximation.Algebra.CoprodIWordInverse import GroupApproximation.Algebra.FiniteIndexQuasiIsometry import GroupApproximation.Algebra.FiniteIndexTransversal import GroupApproximation.Algebra.MorseLemma import GroupApproximation.Algebra.ReidemeisterSchreier import GroupApproximation.Algebra.SchreierGenerators import GroupApproximation.Analysis.CStarOrderZeroSupport import GroupApproximation.Analysis.DadarlatEilers import GroupApproximation.Analysis.KKTheoryKGroups import GroupApproximation.Analysis.KKTheoryKasparov import GroupApproximation.Analysis.KirchbergRordamCorona import GroupApproximation.Analysis.KirchbergRordamEpsilonTest import GroupApproximation.Analysis.KirchbergRordamOrderZeroLift import GroupApproximation.Analysis.TikuisisWhiteWinterProof import GroupApproximation.Analysis.UniversalCoefficientTheorem import GroupApproximation.Higman.AbsorberProgram import GroupApproximation.Higman.BlockTower import GroupApproximation.Higman.NormalClosureProduct import GroupApproximation.Higman.RadicalDirectSum import GroupApproximation.Higman.TowerBlockSearch import GroupApproximation.Higman.TowerCert import GroupApproximation.Higman.TowerComputable import GroupApproximation.Higman.TowerDerivation import GroupApproximation.Kazhdan.InducedRepresentation import GroupApproximation.Kazhdan.KazhdanFiniteIndex import GroupApproximation.Kazhdan.LatticeRouteRemainder import GroupApproximation.Algebra.HyperbolicTransport import GroupApproximation.Analysis.CStarCPStarTarget import GroupApproximation.Analysis.QuasidiagonalTraceLocal import GroupApproximation.Analysis.QuasidiagonalTraceProperties import GroupApproximation.Analysis.TikuisisWhiteWinterCore import GroupApproximation.Computability.TorsionFreeMarkov import GroupApproximation.Computability.TorsionFreeMFMarkov import GroupApproximation.Sofic.IteratedDoubleAmalgam import GroupApproximation.Sofic.SymmetricDoubleCovering import GroupApproximation.Sofic.CoveringWitness import GroupApproximation.Sofic.DoubleFiniteDimensionalRigidity import GroupApproximation.Sofic.DoubleInputsMinimal import GroupApproximation.Sofic.KunThomShulmanDoubleConstruction import GroupApproximation.Sofic.FreeLampKernelSplitting import GroupApproximation.Stability.LinearMetricApproximation import GroupApproximation.Stability.UnnormalizedSchattenApproximation import GroupApproximation.Stability.SchattenNonapproximability import GroupApproximation.Sofic.CentralizerNormalizationRefuted import GroupApproximation.Sofic.GreendlingerDehn import GroupApproximation.Sofic.GreendlingerDehnCritical import GroupApproximation.Sofic.GreendlingerDehnFree import GroupApproximation.Sofic.GreendlingerDehnSwap import GroupApproximation.Algebra.CoprodITorsionFree import GroupApproximation.Algebra.CoprodIWordLength import GroupApproximation.Algebra.CoprodICyclicReduction import GroupApproximation.Algebra.PushoutITorsionFree import GroupApproximation.Algebra.FreeProductFactorQuotient import GroupApproximation.Higman.AmalgamPresentation import GroupApproximation.Higman.AmalgamPushout import GroupApproximation.Higman.CoprodTorsion import GroupApproximation.Higman.HNNCentralizer import GroupApproximation.Higman.BenignAmbient import GroupApproximation.Higman.BenignFamily import GroupApproximation.Higman.BenignJoin import GroupApproximation.Higman.Pinch import GroupApproximation.Higman.Program import GroupApproximation.Higman.EvalRaw import GroupApproximation.Higman.QuotientPresentation import GroupApproximation.Higman.AbsorberGenerators import GroupApproximation.Higman.CodedAbsorber import GroupApproximation.Higman.BlockDecomposition import GroupApproximation.Higman.BlockWordProblem import GroupApproximation.Higman.BlockSearch import GroupApproximation.Higman.BlockComputable import GroupApproximation.Higman.ConjugateBasis import GroupApproximation.Higman.SequenceSpace import GroupApproximation.Higman.BaseCases import GroupApproximation.Higman.Operations import GroupApproximation.Higman.TheoremFour import GroupApproximation.Higman.ShiftOperation import GroupApproximation.Higman.PinchGraph import GroupApproximation.Higman.RopeTorsion import GroupApproximation.Higman.BenignTorsionFree import GroupApproximation.Higman.RowSubgroup import GroupApproximation.Higman.RowBasis import GroupApproximation.Higman.HNNEmbedding import GroupApproximation.Higman.BridgeTorsion import GroupApproximation.Higman.EmbeddingTheorem import GroupApproximation.Higman.ChiodoReduction import GroupApproximation.Higman.RowKernel import GroupApproximation.Higman.HNNDescent import GroupApproximation.Algebra.HNNSubextension import GroupApproximation.Sofic.GreendlingerChunks import GroupApproximation.Sofic.OsinRelativeSmallCancellation import GroupApproximation.Analysis.CStarHilbertModule import GroupApproximation.Analysis.CStarHilbertModuleNorm import GroupApproximation.Analysis.CStarAdjointable import GroupApproximation.Analysis.CStarAdjointableNorm import GroupApproximation.Analysis.CStarPositiveOrder import GroupApproximation.Analysis.PairSumIncidence import GroupApproximation.Analysis.CStarUnitary import GroupApproximation.Analysis.CStarFiniteRank import GroupApproximation.Analysis.CStarCompactOperators import GroupApproximation.Analysis.CStarDirectSumOperators import GroupApproximation.Analysis.CStarModuleDirectSum import GroupApproximation.Analysis.CStarStandardModule import GroupApproximation.Analysis.CStarStandardModuleEquiv import GroupApproximation.Analysis.CStarStabilization import GroupApproximation.Analysis.KasparovBimodule import GroupApproximation.Analysis.KasparovUnitaryEquivalence import GroupApproximation.Sofic.FreeCancellationNesting import GroupApproximation.Kazhdan.OrbitAverageSpectralGap import GroupApproximation.Kazhdan.OrbitAverageFormGap import GroupApproximation.Kazhdan.OrbitAverageFiniteControl import GroupApproximation.Kazhdan.SharpExistenceSpectralRoute import GroupApproximation.Kazhdan.CharTwoTorsionObstruction import GroupApproximation.Kazhdan.SharpExistenceCertificateRoute import GroupApproximation.Algebra.TreeLikeHyperbolic import GroupApproximation.Algebra.BassSerreFreeProductAction import GroupApproximation.Sofic.BassSerreHullGeometry import GroupApproximation.Algebra.ListCommonPrefix import GroupApproximation.Algebra.HyperbolicFreeGroup import GroupApproximation.Kazhdan.FreeGroupSharpProfile import GroupApproximation.Analysis.QuasidiagonalCoronaCriterion import GroupApproximation.Analysis.QuasidiagonalMatricialTrace import GroupApproximation.Analysis.TikuisisWhiteWinterDerivation import GroupApproximation.Higman.HalfRowEndo import GroupApproximation.Higman.IntPrimrec import GroupApproximation.Higman.HigmanPrimitiveRecursion import GroupApproximation.Sofic.BlockInfix import GroupApproximation.Sofic.ConjExprMatching import GroupApproximation.Sofic.MatchingSpine import GroupApproximation.Sofic.NonCrossingMatching import GroupApproximation.Sofic.RelatorBlock import GroupApproximation.Algebra.HNNBridgeAmbient import GroupApproximation.Algebra.HNNBridgeFamily import GroupApproximation.Higman.AddRelators import GroupApproximation.Higman.FinalReduction import GroupApproximation.Higman.REPredNormalForm import GroupApproximation.Higman.RecursivePresentationBridge import GroupApproximation.Higman.RelatorEnumeration import GroupApproximation.Higman.RelatorRE import GroupApproximation.Sofic.GreendlingerBeyond import GroupApproximation.Algebra.HNNBridgeFreeness import GroupApproximation.Algebra.HNNBridgeTorsionFree import GroupApproximation.Analysis.CStarCompactSelfModule import GroupApproximation.Analysis.ConvexUnitVectorRigidity import GroupApproximation.Sofic.GreendlingerMaxConjugator import GroupApproximation.Sofic.OrderPreservingDegeneracy import GroupApproximation.Sofic.BareDefectSource import GroupApproximation.Sofic.SingleDefectSaturation import GroupApproximation.Sofic.ArithmeticSingleDefectEndpoint import GroupApproximation.Algebra.CongruenceTorsionFree import GroupApproximation.Kazhdan.SL3Certificate import GroupApproximation.Sofic.BespokeRouterConstruction import GroupApproximation.Algebra.FreeGroupFiniteRank import GroupApproximation.Kazhdan.TorsionFreeKazhdanPartner import GroupApproximation.Algebra.SteinbergSL3 import GroupApproximation.Algebra.FinitePresentationFiniteIndex import GroupApproximation.Sofic.PeriodicOverlap import GroupApproximation.Sofic.FreeProductRouterObstruction import GroupApproximation.Sofic.GreendlingerDeepestMatch import GroupApproximation.Sofic.GreendlingerCoincidence import GroupApproximation.Sofic.GreendlingerBetaBranch import GroupApproximation.Sofic.GreendlingerAlphaPlumb import GroupApproximation.Sofic.GreendlingerDeepArc import GroupApproximation.Sofic.GreendlingerDeepVacuity import GroupApproximation.Sofic.GreendlingerPieceOverlapProof import GroupApproximation.Sofic.GreendlingerSharpTwins import GroupApproximation.Sofic.GreendlingerDeepVacuitySharp import GroupApproximation.Sofic.GreendlingerDeepThreeFactor import GroupApproximation.Sofic.GreendlingerDeepInduction import GroupApproximation.Sofic.GreendlingerDeepTailWindow import GroupApproximation.Sofic.GreendlingerSharpWindow import GroupApproximation.Sofic.GreendlingerSharpRigidity import GroupApproximation.Sofic.GreendlingerSharpBackLoss import GroupApproximation.Sofic.GreendlingerSharpReduction import GroupApproximation.Sofic.GreendlingerSharpDropGate import GroupApproximation.Sofic.GreendlingerSharpDeepArc import GroupApproximation.Sofic.GreendlingerSharpChunks import GroupApproximation.Sofic.GreendlingerSharpLandingAux import GroupApproximation.Sofic.GreendlingerSharpThreeFactor import GroupApproximation.Sofic.GreendlingerSharpInduction import GroupApproximation.Sofic.GreendlingerSharpOverlap import GroupApproximation.Sofic.GreendlingerSharpLandingProd import GroupApproximation.Sofic.GreendlingerSharpInvariant import GroupApproximation.Sofic.GreendlingerSharpWindowDrop import GroupApproximation.Sofic.GreendlingerSharpDehn import GroupApproximation.Sofic.GreendlingerSharpMinimal import GroupApproximation.Sofic.GreendlingerSharpRegime import GroupApproximation.Sofic.GreendlingerDeepInvariant import GroupApproximation.Sofic.GreendlingerLandingConfined import GroupApproximation.Sofic.GreendlingerRelativeTransfer import GroupApproximation.Sofic.GreendlingerSharpResidualWiring import GroupApproximation.Sofic.GreendlingerSharpResidualWiring2 import GroupApproximation.Sofic.GreendlingerDeepOverrunCount import GroupApproximation.Sofic.GreendlingerLandingProd import GroupApproximation.Sofic.GreendlingerSharpLandingProduction import GroupApproximation.Sofic.GreendlingerSharpHeadLanding import GroupApproximation.Sofic.GreendlingerCompositeWellPosed import GroupApproximation.Sofic.GreendlingerNoDeepCollapse import GroupApproximation.Sofic.GreendlingerEmptyConjCorner import GroupApproximation.Sofic.GreendlingerCollapseInduction import GroupApproximation.Sofic.GreendlingerCyclicTwoArc import GroupApproximation.Sofic.SymmetricDoubleMF import GroupApproximation.Sofic.LiteralAffineFreeProductSource import GroupApproximation.Sofic.LiteralAffineHullCommonQuotientInput import GroupApproximation.Sofic.LiteralAffineHullTwoStageBridge import GroupApproximation.Sofic.LiteralAffineFreeProductBassSerre import GroupApproximation.Sofic.LiteralAffineFreeProductBassSerreDisplacement import GroupApproximation.Sofic.LiteralAffineFreeProductBassSerreIndependence import GroupApproximation.Kazhdan.TriangularHodgeLayer import GroupApproximation.Sofic.OsinWeightedDefectNoGo import GroupApproximation.Sofic.OsinWeightedLeafNoGo import GroupApproximation.Sofic.TorsionDescent import GroupApproximation.Leavitt.HilbertHotelBlocks import GroupApproximation.Leavitt.HilbertHotelSaturation import GroupApproximation.Leavitt.HilbertHotelWhitehead import GroupApproximation.Leavitt.HilbertHotelBinary import GroupApproximation.Leavitt.HilbertHotelDefectNormal import GroupApproximation.Leavitt.HilbertHotelCover import GroupApproximation.Leavitt.ConjProductClosure import GroupApproximation.Leavitt.HilbertHotelCoverDischarges import GroupApproximation.Leavitt.HilbertHotelModelNonMF import GroupApproximation.Leavitt.HilbertHotelCoverBlock import GroupApproximation.Leavitt.HilbertHotelEndpoint import GroupApproximation.Sofic.MFCamouflage import GroupApproximation.Sofic.MFCamouflageRadical import GroupApproximation.Sofic.MFCamouflageConsequences import GroupApproximation.Higman.CoordCalculus import GroupApproximation.Higman.SeqFilter import GroupApproximation.Higman.AgreeClosure import GroupApproximation.Higman.OmegaClosure import GroupApproximation.Higman.OperationClosureRho import GroupApproximation.Higman.TorsionFreeImageClosure import GroupApproximation.Higman.ClosuresAssembly import GroupApproximation.Higman.AmalgamTorsionDischarge import GroupApproximation.Higman.TheoremThreeAssembly import GroupApproximation.Higman.EnumeratedRange import GroupApproximation.Higman.EnumeratedRangeTrace import GroupApproximation.Higman.EnumeratedRangeTraceCorrectness import GroupApproximation.Higman.EnumeratedRangeProjection import GroupApproximation.Higman.EnumeratedRangeVerify import GroupApproximation.Higman.TraceRelationRE import GroupApproximation.Higman.HigmanCodingDictionary import GroupApproximation.Higman.HigmanAtoms import GroupApproximation.Higman.HigmanVariableCalculus import GroupApproximation.Higman.TransportFive import GroupApproximation.Higman.TransportStar import GroupApproximation.Higman.TransportStarWitness import GroupApproximation.Higman.MapEmbSharp import GroupApproximation.Higman.BridgeEffectivity import GroupApproximation.Higman.BridgeWordProblem import GroupApproximation.Higman.CentralHNNFreeLabelAction import GroupApproximation.Higman.CentralHNNFreeLabelFaithful import GroupApproximation.Higman.CentralHNNFreeLabelKernel import GroupApproximation.Higman.OmegaTower import GroupApproximation.Higman.OmegaTowerStages import GroupApproximation.Higman.OmegaTowerDescent import GroupApproximation.Higman.OmegaTowerStageTwo import GroupApproximation.Higman.OmegaTowerStageThree import GroupApproximation.Higman.OmegaTowerClassifiedPinchStep import GroupApproximation.Higman.OmegaTowerInterfaceCounterexample import GroupApproximation.Higman.OmegaTowerRightTailCollapse import GroupApproximation.Higman.OmegaTowerRightTailSubgroup import GroupApproximation.Higman.OmegaTowerStaticSeamFreeCoordinates import GroupApproximation.Higman.RowDeletionBenign import GroupApproximation.Higman.SwapWitnessTower import GroupApproximation.Higman.SwapCarrierFromTower import GroupApproximation.Higman.SwapCarrierWitness import GroupApproximation.Higman.TauRouteC import GroupApproximation.Higman.SsetBaseCase import GroupApproximation.Higman.CurrentOperationClosures import GroupApproximation.Higman.CurrentREBenign import GroupApproximation.Higman.OmegaDebt import GroupApproximation.Higman.OperationClosureTheta import GroupApproximation.Higman.OperationClosureTau import GroupApproximation.Higman.FlipGroup import GroupApproximation.Higman.AmalgamTorsion import GroupApproximation.Higman.GeneratedBasic import GroupApproximation.Higman.GeneratedCoords import GroupApproximation.Higman.GeneratedPin import GroupApproximation.Higman.GeneratedValue import GroupApproximation.Higman.GeneratedTransition import GroupApproximation.Higman.GeneratedEnumeration import GroupApproximation.Sofic.LiteralTorsionFreeRouterSourceNoGo import GroupApproximation.Sofic.LiteralAffineFreeProductAvatarBlueprint import GroupApproximation.Higman.LiteralAffineFreeProductPaddedAvatarBlueprint import GroupApproximation.Higman.LiteralAffineFreeProductAvatarChecks import GroupApproximation.Sofic.AvatarRouterInstance import GroupApproximation.Sofic.AvatarRunBound import GroupApproximation.Sofic.BespokeRouterGateAssembly import GroupApproximation.Sofic.GreendlingerFreeGate import GroupApproximation.Sofic.GreendlingerReducedness import GroupApproximation.Sofic.AmalgamMFTrace import GroupApproximation.Sofic.TerminalQuotientPresentation import GroupApproximation.Sofic.TerminalQuotientIso import GroupApproximation.Sofic.SigmaGroupMF import GroupApproximation.Sofic.SymmetricDoubleShulman import GroupApproximation.Sofic.PushedDefectSaturation import GroupApproximation.Sofic.ArithmeticAmplifiedEndpoint import GroupApproximation.Sofic.MinimalNoCancellingPair import GroupApproximation.Sofic.MinimalPalindromePair import GroupApproximation.Sofic.MatchingReduced import GroupApproximation.Sofic.MatchingPositions import GroupApproximation.Sofic.MatchingBoundaryBlock import GroupApproximation.Sofic.MatchingRunPiece import GroupApproximation.Sofic.MatchingStemContraction import GroupApproximation.Sofic.CurvatureAssembly import GroupApproximation.Sofic.MatchingRunGap import GroupApproximation.Sofic.ShellSingleRegion import GroupApproximation.Sofic.RadicalAutomorphization import GroupApproximation.Endpoint.ApproximationRadicals import GroupApproximation.Sofic.MatchingSameBlock import GroupApproximation.Sofic.MatchingRunStructure import GroupApproximation.Sofic.MatchingStemFold import GroupApproximation.Sofic.SigmaCompressionPair import GroupApproximation.Computability.MFRecognitionImpossible import GroupApproximation.Endpoint.MFRecognitionAudit import GroupApproximation.Sofic.PalindromicMinimalExpr import GroupApproximation.Sofic.MatchingFactorPair import GroupApproximation.Sofic.NonCrossingEdgeBound import GroupApproximation.Sofic.NonCrossingDegreeBound import GroupApproximation.Sofic.MatchingChordGraph import GroupApproximation.Sofic.CurvatureStemThreshold import GroupApproximation.Sofic.MatchingFoldObstruction import GroupApproximation.Sofic.MatchingBlockOrder import GroupApproximation.Computability.CodedMicrostate import GroupApproximation.Computability.MicrostateNormalForm import GroupApproximation.Computability.RationalComplexCode import GroupApproximation.Computability.EffectiveMatrixCode import GroupApproximation.Analysis.OperatorNormCertificate import GroupApproximation.Analysis.CayleyUnitary import GroupApproximation.Analysis.UnitaryPerturbation import GroupApproximation.Analysis.RationalHermitian import GroupApproximation.Analysis.RatComplexSubfield import GroupApproximation.Analysis.AdjointDefectEstimate import GroupApproximation.Manuscript.OneSidedMFRadical.TransportAssembly import GroupApproximation.Manuscript.OneSidedMFRadical.CanonicalSector import GroupApproximation.Manuscript.OneSidedMFRadical.HeadlineTheorem import GroupApproximation.Endpoint.OneSidedTransportAudit import GroupApproximation.Leavitt.RankTwelveCorner import GroupApproximation.Leavitt.LeavittMarkNontrivial import GroupApproximation.Kazhdan.AmenableKazhdanFinite import GroupApproximation.Kazhdan.KazhdanSeparableDescent import GroupApproximation.Leavitt.BinaryLeavittSimple import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedLeavittEquations import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedDefinitions import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedRemarks import GroupApproximation.Manuscript.OneSidedMFRadical.CountableNonMF import GroupApproximation.Leavitt.ElementarySimplicity import GroupApproximation.Manuscript.OneSidedMFRadical.CornerCoronaClass import GroupApproximation.Leavitt.CongruenceSubgroups import GroupApproximation.Leavitt.ElementaryTransvectionExtraction import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedSectorProof import GroupApproximation.Leavitt.RootDetectionBinary import GroupApproximation.Leavitt.DiagonalNormalExtraction import GroupApproximation.Manuscript.OneSidedMFRadical.CornerCoordinatePassage import GroupApproximation.Manuscript.OneSidedMFRadical.SentenceClosureAudit import GroupApproximation.Manuscript.OneSidedMFRadical.SentenceCurrentLeavittCompressionClosure import GroupApproximation.Manuscript.OneSidedMFRadical.HNNCoronaConjugatorSentenceAudit import GroupApproximation.Manuscript.OneSidedMFRadical.HNNAmalgamCornerSentences import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationMFEndpoint import GroupApproximation.Manuscript.OneSidedMFRadical.ComputabilityConstructionClosure import GroupApproximation.Manuscript.OneSidedMFRadical.CompleteDefectSaturation import GroupApproximation.Manuscript.OneSidedMFRadical.TransportCommutantEquality import GroupApproximation.Leavitt.ExchangeRefinement import GroupApproximation.Leavitt.RowAnnihilatorTransvection import GroupApproximation.Leavitt.PreusserSandwichStep import GroupApproximation.Leavitt.PreusserAssembly import GroupApproximation.Leavitt.PreusserLevelUniqueness import GroupApproximation.Leavitt.PreusserNormalizedByCore import GroupApproximation.Leavitt.PreusserNormalizedByRowAnnihilator import GroupApproximation.Leavitt.PreusserNormalizedBySandwich import GroupApproximation.Leavitt.PreusserNormalizedBy import GroupApproximation.Steinberg.GeneralRankElementaryPropertyT import GroupApproximation.Steinberg.ElementaryIndexPadding import GroupApproximation.Steinberg.GeneralRankFiniteFieldPropertyT import GroupApproximation.PropertyT.A2MagicExponentFree import GroupApproximation.PropertyT.FinitelyGeneratedRing import GroupApproximation.PropertyT.FinitelyGeneratedRingPermanence import GroupApproximation.PropertyT.EJZIntegralReduction import GroupApproximation.PropertyT.EJZIntegralGeneralRankReduction import GroupApproximation.Leavitt.RowAnnihilatorAlternate import GroupApproximation.PropertyT.IntegralCharacterMass import GroupApproximation.PropertyT.IntegralColumnPlaneReduction import GroupApproximation.PropertyT.IntegralColumnPlaneRootReduction import GroupApproximation.PropertyT.IntegralColumnPlaneSpectralShear import GroupApproximation.PropertyT.IntegralColumnPlaneSpectralTorus import GroupApproximation.PropertyT.IntegralColumnPlaneSpectralCoreBound import GroupApproximation.PropertyT.IntegralColumnPlaneSpectralMassBound import GroupApproximation.PropertyT.KassabovRankZeroTorusGeometry import GroupApproximation.PropertyT.IntegralScalarRootDisplacement import GroupApproximation.PropertyT.IntegralPolynomialDisplacement import GroupApproximation.PropertyT.KassabovMeasureInequalities import GroupApproximation.PropertyT.KassabovBorelMeasureInequalities import GroupApproximation.PropertyT.KassabovTorusNumerics import GroupApproximation.Analysis.CommutativeCStarCovariance import GroupApproximation.Analysis.CommutativeStateSpectralMeasure import GroupApproximation.Analysis.HilbertQuadraticTransport import GroupApproximation.Analysis.RepresentedRootPlaneSpectralMeasure import GroupApproximation.Kazhdan.RealToComplexUnitaryRepresentation import GroupApproximation.PropertyT.ExponentFreeClassTwoOrthogonality import GroupApproximation.PropertyT.HeisenbergAngleBound import GroupApproximation.Computability.FiniteDimensionalApproximationIncomplete import GroupApproximation.Computability.ArithmeticalHierarchy import GroupApproximation.Computability.FixedMarkedQueryHierarchy import GroupApproximation.Computability.FixedLiteralMarkedQuery import GroupApproximation.Computability.ExactSwitchQueryCompleteness import GroupApproximation.Computability.ExactSwitchAlgorithmicConsequences import GroupApproximation.Computability.FixedLiteralMarkedQueryFiniteHardness import GroupApproximation.Computability.EnumeratedFixedMarkedQueryConsequences import GroupApproximation.Computability.MicrostateNaturalize import GroupApproximation.Endpoint.MFComputabilityPaperAudit import GroupApproximation.Sofic.SplitMFStability import GroupApproximation.Sofic.MFBlackHoleAttachment import GroupApproximation.Sofic.InvisibleExtensions import GroupApproximation.Endpoint.InvisibleExtensionsAudit import GroupApproximation.Analysis.KOmegaHilbertSpaceEndpoint import GroupApproximation.Analysis.ReducedGroupCStarStablyFinite import GroupApproximation.Analysis.ReducedGroupCStarMFAlgebra import GroupApproximation.Analysis.ReducedGroupCStarDedekindFinite import GroupApproximation.Analysis.BlackadarKirchbergFiniteDimensionalLift import GroupApproximation.Analysis.BlackadarKirchbergFiniteDirectSumLift import GroupApproximation.Analysis.BlackadarKirchbergStarEquivTransport import GroupApproximation.Analysis.GoldbringHartRoute import GroupApproximation.Manuscript.OneSidedMFRadical.ReducedCStarConsequence import GroupApproximation.Manuscript.OneSidedMFRadical.ReducedCStarNotNuclear import GroupApproximation.Computability.HereditaryPropertySwitchCompleteness import GroupApproximation.Computability.HyperlinearMarkov import GroupApproximation.Computability.HereditaryRecognitionPhaseDiagram import GroupApproximation.Computability.HyperlinearRecognitionSecondLevel import GroupApproximation.Computability.HyperlinearRecognitionHierarchy import GroupApproximation.Computability.MarkovRecognitionHierarchy import GroupApproximation.Analysis.FiniteMatrixAnisotropicSign import GroupApproximation.Analysis.FiniteMatrixSignNormalization import GroupApproximation.Computability.FreeEdgeTowerCodePrimrec import GroupApproximation.Computability.FreeEdgeTowerSemantics import GroupApproximation.Computability.FreeEdgeTowerIteration import GroupApproximation.Computability.EffectiveMatrixVectorWitnessComplete import GroupApproximation.Computability.MFRecognitionPi02 import GroupApproximation.Computability.MFRecognitionSecondLevel import GroupApproximation.Endpoint.MFRecognitionSecondLevelAudit import GroupApproximation.Endpoint.MFEnumeratedPi02Audit import GroupApproximation.Computability.MicrostateGeneratorEncoding import GroupApproximation.Computability.SoficPromiseMFRecognition import GroupApproximation.External.TauCeti.RepresentationTheory.Compact.RepresentativeDensity import GroupApproximation.Higman.InjectedCompilerTower import GroupApproximation.Higman.MikhailovaFiberProduct import GroupApproximation.Higman.MikhailovaFiberProductProfinite import GroupApproximation.Higman.MikhailovaGraphProductWitness import GroupApproximation.Higman.MikhailovaRankThreeWitness import GroupApproximation.Higman.MikhailovaRopeCode import GroupApproximation.Higman.MikhailovaRankThreeCode import GroupApproximation.Higman.MikhailovaRopeCodeSemantics import GroupApproximation.Higman.MikhailovaRopeCompiler import GroupApproximation.Higman.PairedReturnCutterCode import GroupApproximation.Higman.PairedReturnMapEmbCode import GroupApproximation.Higman.TransportStarCode import GroupApproximation.Endpoint.PairedReturnCutterCodeAudit import GroupApproximation.Higman.FreeLampFinitePresentation import GroupApproximation.Higman.PairedFoldKernel import GroupApproximation.Higman.PairedReturnFirstIntersection import GroupApproximation.Higman.PairedReturnGraphIntersection import GroupApproximation.Higman.MatchedSubgroupAmalgam import GroupApproximation.Higman.PairedReturnCutter import GroupApproximation.Higman.PairedReturnEdgeGraph import GroupApproximation.Higman.PairedReturnEdgeProfinite import GroupApproximation.Higman.PairedReturnFirstRangeVirtualRetract import GroupApproximation.Higman.PairedReturnAmbientResiduallyFinite import GroupApproximation.Higman.TransportCodeRE import GroupApproximation.Leavitt.LeavittModuleRank import GroupApproximation.Manuscript.OneSidedMFRadical.CornerClassIdentificationAudit import GroupApproximation.Computability.SoficRecognitionSecondLevel import GroupApproximation.Manuscript.NonMF.AcylindricallyHyperbolic import GroupApproximation.Manuscript.NonMF.HullSmallCancellation import GroupApproximation.Manuscript.MFRecognition.MarkedHigmanOutput import GroupApproximation.Manuscript.MFRecognition.EffectiveHigmanCompiler import GroupApproximation.Manuscript.MFRecognition.LocalityAndCertificates import GroupApproximation.Manuscript.MFRecognition.FinitelyGeneratedNonMFQuotient import GroupApproximation.Manuscript.MFRecognition.SeedPresentation import GroupApproximation.Manuscript.MFRecognition.ReducedProductsWiring import GroupApproximation.Manuscript.NonMF.Saturation import GroupApproximation.Manuscript.MFRecognition.MikhailovaConsequences import GroupApproximation.Manuscript.OneSidedMFRadical.RankTwelveSimplicitySentences import GroupApproximation.Manuscript.OneSidedMFRadical.LeavittSectionSentences import GroupApproximation.Manuscript.MFRecognition.RopeObjects import GroupApproximation.Manuscript.MFRecognition.CentralRope import GroupApproximation.Manuscript.NonMF.PriorWorkBlackadarKirchberg import GroupApproximation.Manuscript.NonMF.PriorWorkConnesEmbedding import GroupApproximation.Manuscript.NonMF.PriorWorkErshovJaikinZapirain import GroupApproximation.Manuscript.NonMF.PriorWorkShulmanAmalgam import GroupApproximation.Manuscript.MFRecognition.TensorSynchronizationCoronaTrace import GroupApproximation.Manuscript.OneSidedMFRadical.StableFinitenessSentencesCore import GroupApproximation.Manuscript.OneSidedMFRadical.StableFinitenessSentences import GroupApproximation.Manuscript.NonMF.FournierFacioDoubleHNN import GroupApproximation.Manuscript.NonMF.FournierFacioInput import GroupApproximation.Manuscript.NonMF.TorsionFreeTheoremC import GroupApproximation.Manuscript.MFRecognition.FiniteRope import GroupApproximation.Manuscript.MFRecognition.ThreeGeneratorBridgeRecursive import GroupApproximation.Manuscript.MFRecognition.ThreeGeneratorBridgeInjective import GroupApproximation.Manuscript.MFRecognition.RopeObjectsProfinite import GroupApproximation.Manuscript.OneSidedMFRadical.NormalKazhdanSentences import GroupApproximation.Manuscript.OneSidedMFRadical.RadicalCalculusSentences import GroupApproximation.Manuscript.OneSidedMFRadical.IntroductionClaimSentences import GroupApproximation.Manuscript.OneSidedMFRadical.KazhdanTransportSentences import GroupApproximation.Manuscript.MFRecognition.ReducedProductsPermanenceWiring import GroupApproximation.Manuscript.MFRecognition.ThreeGeneratorBridge import GroupApproximation.Manuscript.MFRecognition.ThreeGeneratorBridgeNormalCore import GroupApproximation.Manuscript.MFRecognition.ThreeGeneratorBridgeQuotient import GroupApproximation.Manuscript.MFRecognition.RecognitionInputs import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceDischarge import GroupApproximation.Manuscript.MFRecognition.BridgeUniformPresentation import GroupApproximation.Manuscript.MFRecognition.CentralRopeGenerators import GroupApproximation.Manuscript.MFRecognition.PositiveBranchStableLetterRemark import GroupApproximation.Manuscript.MFRecognition.SeedLemma import GroupApproximation.Manuscript.MFRecognition.RopeRecognitionInputs import GroupApproximation.Manuscript.MFRecognition.RecognitionAssembly import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerProof import GroupApproximation.Manuscript.MFRecognition.RopeCodeFamilyConstruction import GroupApproximation.Manuscript.MFRecognition.RopeCodeFamilySemantics import GroupApproximation.Analysis.ShulmanFillTheorem16 import GroupApproximation.Analysis.ShulmanFillConjugatePair import GroupApproximation.Analysis.MFAlgebraAmalgamFactorMap import GroupApproximation.Analysis.MFAlgebraAmalgamFactorMapProperties import GroupApproximation.Analysis.MFAlgebraAmalgamFactorRepresentation import GroupApproximation.Analysis.MFAlgebraSymmetricDoubleIdentity import GroupApproximation.Analysis.CompatibleCoronaSupportCorner import GroupApproximation.Analysis.ShulmanFillConjugationEstimate import GroupApproximation.Analysis.ShulmanFillModelDescent import GroupApproximation.Analysis.ShulmanFillAsymptoticGlue import GroupApproximation.Analysis.ShulmanFillCommutantExact import GroupApproximation.Analysis.ShulmanFillSymmetricDoubleFlip import GroupApproximation.Analysis.ShulmanFillDiagonalHom import GroupApproximation.Analysis.ShulmanFillCommutantUnitary import GroupApproximation.Analysis.ShulmanFillCoronaJoin import GroupApproximation.Analysis.ShulmanFillCoronaPair import GroupApproximation.Analysis.ShulmanFillUnitalCorner import GroupApproximation.Analysis.ShulmanFillWordLimsup import GroupApproximation.Analysis.ShulmanSymmetricDoubleRoute import GroupApproximation.Analysis.ShulmanFillSymmetricDouble import GroupApproximation.Analysis.ShulmanFillSymmetricDoubleEmbedTheorem13 import GroupApproximation.Analysis.ShulmanFillSymmetricDoubleEmbed import GroupApproximation.Analysis.ShulmanFillTheorem13 import GroupApproximation.Analysis.ShulmanFillFaithfulPairCollapse import GroupApproximation.Analysis.CalkinCompactIdeal import GroupApproximation.Analysis.CalkinSchauder import GroupApproximation.Analysis.CalkinSchauderProof import GroupApproximation.Analysis.CStarQuotient import GroupApproximation.Analysis.CalkinAlgebra import GroupApproximation.Analysis.CalkinAlgebraStar import GroupApproximation.Analysis.CalkinCStarAlgebra import GroupApproximation.Analysis.StarStrongMatrixSequences import GroupApproximation.Analysis.StarStrongMatrixSequencesAlgebra import GroupApproximation.Analysis.StarStrongLimitNorm import GroupApproximation.Analysis.StarStrongMatrixSequencesShulman import GroupApproximation.Analysis.ArvesonBHTarget import GroupApproximation.Analysis.VoiculescuPlan import GroupApproximation.Analysis.StarStrongBlockModel import GroupApproximation.Analysis.EllTwoBlockFamily import GroupApproximation.Analysis.ArvesonWeakLimit import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceNonunital import GroupApproximation.Manuscript.MFRecognition.EffectiveCompilerOfOmega import GroupApproximation.Manuscript.OneSidedMFRadical.PrintedForms import GroupApproximation.Manuscript.NonMF.TheoremCPrinted import GroupApproximation.Manuscript.NonMF.HullBallForm import GroupApproximation.Manuscript.NonMF.TheoremCDebts import GroupApproximation.Manuscript.NonMF.ChiodoOfHigman import GroupApproximation.Manuscript.NonMF.HullInputsProved import GroupApproximation.Manuscript.NonMF.HullFillKernelRefutation import GroupApproximation.Manuscript.NonMF.HullFillCorrectedInputs import GroupApproximation.Manuscript.NonMF.HullFillTheoremCCorrected import GroupApproximation.Manuscript.MFRecognition.SeedFromTheoremC import GroupApproximation.Manuscript.MFRecognition.SeedRemarkTheoremC import GroupApproximation.Manuscript.MFRecognition.RecognitionDebts import GroupApproximation.Manuscript.MFRecognition.CentralRopeBritton import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceSetup import GroupApproximation.Manuscript.MFRecognition.MarkedHigmanRopeInput import GroupApproximation.Manuscript.MFRecognition.MarkedHigmanRopeProfinite import GroupApproximation.Manuscript.MFRecognition.CentralRopeCore import GroupApproximation.Manuscript.MFRecognition.NegativeBranch import GroupApproximation.Manuscript.MFRecognition.PositiveBranchFiniteQuotients import GroupApproximation.Analysis.ContinuousImageClosure import GroupApproximation.Analysis.StarSubalgebraMapEquiv import GroupApproximation.Manuscript.MFRecognition.TensorSynchronizationData import GroupApproximation.Manuscript.MFRecognition.TensorSynchronizationConjugator import GroupApproximation.Analysis.ContinuousAdjoinMapping import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceSetupPrelude import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceSetupEdges import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeConjugationDef import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientDef import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientGenerators import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientContinuous import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientClosureForward import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientClosureBackward import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientClosure import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceBaseToCoronaInjective import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceSourceAmbientMap import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceTargetAmbientMap import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientMaps import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientRestriction import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceConstructedEdgeDef import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceConstructedEdgeConj import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceConstructedEdgeGenerator import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeAmbientEquiv import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeIso import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeCovariance import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceCoronaRepresentation import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUniversalDef import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUniversalMapping import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceSetupUniversal import GroupApproximation.Manuscript.MFRecognition.SwitchGroupBCRRelators import GroupApproximation.Manuscript.MFRecognition.CompilerIntroSentences import GroupApproximation.Manuscript.MFRecognition.TensorSynchronization import GroupApproximation.Manuscript.MFRecognition.SwitchGroupBCR import GroupApproximation.Manuscript.MFRecognition.CoronaEmbeddingRemark import GroupApproximation.Manuscript.MFRecognition.RegularRealizationSentences import GroupApproximation.Manuscript.ClosureAssumptionAudit import GroupApproximation.Manuscript.MFRecognition.PreliminarySentences import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGroupData import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationMatrixCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationCoordinateCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationCoronaCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationMFCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGeneratedCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationCoordinateConjugatorCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationProductConjugatorCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationConjugatorCore import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaOperations import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaBasicMaps import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCoronaFactors import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCompatibility import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaFactorMaps import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaRepresentation import GroupApproximation.Analysis.HNNTraceGeneratedDensity import GroupApproximation.Analysis.HNNTraceStarAlgHomDescent import GroupApproximation.Analysis.HNNTraceTracialStateContinuous import GroupApproximation.Manuscript.MFRecognition.HNNTraceBaseTransport import GroupApproximation.Manuscript.MFRecognition.TensorSynchronizationSentences import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceCitations import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceTraceBridge import GroupApproximation.Manuscript.MFRecognition.HNNPermanence import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaAmalgamPackage import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaAmalgamLeft import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaAmalgamRight import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaAmalgamInjective import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaAmalgamCommonImage import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaMatrixIdentities import GroupApproximation.Manuscript.MFRecognition.HNNTraceBaseTrace import GroupApproximation.Manuscript.MFRecognition.HNNTraceReducedFactorization import GroupApproximation.Manuscript.MFRecognition.HNNTraceReducedAlongMap import GroupApproximation.Manuscript.MFRecognition.HNNTraceReducedAlongTrace import GroupApproximation.Manuscript.MFRecognition.HNNTraceReducedSurjection import GroupApproximation.Manuscript.MFRecognition.HNNTraceReducedSubgroupCore import GroupApproximation.Manuscript.MFRecognition.HNNTraceReducedSubgroup import GroupApproximation.Manuscript.MFRecognition.HNNTraceCovariantBase import GroupApproximation.Manuscript.MFRecognition.PositiveBranch import GroupApproximation.Manuscript.MFRecognition.RecognitionMainTheorem import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceEdgeDensity import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerUnit import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaMatrixUnitLeft import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaLeftMatrixIdentityEleven import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaElevenLeftInclusion import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaMatrixUnitRight import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaRightMatrixIdentityEleven import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaElevenRightInclusion import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerUnitEleven import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerUnitLeft import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerMatrixIdentity import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerUnitLeftInclusion import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerUnitLeftCommon import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerUnitCommonImage import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaRightMatrixIdentity import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerUnitRightInclusion import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerUnitRight import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerCommonImages import GroupApproximation.Manuscript.NinetyNineProblems.StablyFinite import GroupApproximation.Manuscript.NinetyNineProblems.ProblemX import GroupApproximation.Manuscript.NinetyNineProblems.ProblemXImpliesIX import GroupApproximation.Manuscript.NinetyNineProblems.FactorizationProperty import GroupApproximation.Manuscript.NinetyNineProblems.ProblemXGroups import GroupApproximation.Manuscript.NinetyNineProblems.FactorizationImpliesHyperlinear import GroupApproximation.Analysis.MatrixAbsoluteValue import GroupApproximation.Analysis.HilbertSchmidtPolarCorrection import GroupApproximation.Analysis.CStarMatrixTwoCorner import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedConjugator import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedFactorDefs import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedCovariance import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedCompatibilityApply import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedCompatibility import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedRepresentation import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedAmalgamMap import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedAmalgamProperties import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerWord import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaBaseCornerElement import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaBaseCornerMap import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerCovarianceAmbient import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerStableUnitary import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerCovariance import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerNontrivial import GroupApproximation.Analysis.AmenableTraceHyperlinear import GroupApproximation.Manuscript.NinetyNineProblems.FactorizationHyperlinearTheorem import GroupApproximation.Manuscript.NinetyNineProblems.KazhdanQuasidiagonalTraces import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedCornerDef import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedCornerBase import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaUniversalMapDef import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaUniversalMapProperties import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedCornerStable import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaEvaluatedComposite import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaDirectEmbedding import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCitation import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceShulman import GroupApproximation.Algebra.CoprodIAltWord import GroupApproximation.Analysis.NormMatrixCoronaPolynomialLifts import GroupApproximation.Analysis.RationalNoncommutativeStarPolynomial import GroupApproximation.Analysis.RationalStarPolynomialBlockDiagonal import GroupApproximation.Analysis.ReducedProductMFBlockDiagonal import GroupApproximation.Analysis.ReducedProductMFDiagonalData import GroupApproximation.Analysis.ReducedProductMFFiniteSelection import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationAssembly import GroupApproximation.Analysis.BoundedCStarSequenceAlgebraEvaluation import GroupApproximation.Analysis.BoundedCStarSequenceEvaluation import GroupApproximation.Analysis.BoundedCStarSequenceEvaluationDef import GroupApproximation.Analysis.CStarCountableAdjoinSeparable import GroupApproximation.Analysis.CStarGeneratedClosureEquality import GroupApproximation.Analysis.CStarGeneratedSeparable import GroupApproximation.Analysis.CStarGeneratedSeparableCountable import GroupApproximation.Analysis.CStarGeneratedSeparableUnion import GroupApproximation.Analysis.DenseRationalStarPolynomialExtension import GroupApproximation.Analysis.ReducedProductMFDesignatedCoordinate import GroupApproximation.Analysis.ShulmanCoronaHalmosArgumentCommutator import GroupApproximation.Analysis.ShulmanCoronaHalmosDef import GroupApproximation.Analysis.ShulmanCoronaHalmosDefectRoot import GroupApproximation.Analysis.ShulmanHalmosDilationAlgebra import GroupApproximation.Analysis.ShulmanHalmosDilationBase import GroupApproximation.Analysis.ShulmanHalmosDilationCommutator import GroupApproximation.Analysis.ShulmanHalmosDilationDef import GroupApproximation.Analysis.ShulmanHalmosDilationDefectPositive import GroupApproximation.Analysis.ShulmanHalmosDilationDiagNonneg import GroupApproximation.Analysis.ShulmanHalmosDilationEndpoint import GroupApproximation.Analysis.ShulmanHalmosDilationUnitary import GroupApproximation.Analysis.StarSubalgebraMapEquivDef import GroupApproximation.Analysis.StarSubalgebraRestrictionEquiv import GroupApproximation.Computability.BenignComapCodeSemantics import GroupApproximation.Higman.OmegaTowerConjugateBasisCoordinates import GroupApproximation.Higman.OmegaTowerConjugateBasisEdge import GroupApproximation.Higman.OmegaTowerConjugateBasisInvariant import GroupApproximation.Higman.OmegaTowerConjugateBasisPinch import GroupApproximation.Higman.OmegaTowerConjugateBasisPinchRewrite import GroupApproximation.Higman.OmegaTowerConjugateBasisShift import GroupApproximation.Higman.OmegaTowerConjugateBasisUnshift import GroupApproximation.Higman.OmegaTowerLocalGlobalCoordinates import GroupApproximation.Higman.OmegaTowerShiftSeam import GroupApproximation.Higman.OmegaTowerSignedShift import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaAmalgamPackageType import GroupApproximation.Manuscript.MFRecognition.ThreeGeneratorBridgeEffectivity import GroupApproximation.Manuscript.MFRecognition.ThreeGeneratorBridgePresentation import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGeneratedCovarianceCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGeneratedDefinitionCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGeneratedEndpointCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGeneratedInstanceCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGeneratedRestrictionCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGeneratedSeparableCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationGeneratedSubalgebraCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationMFCoordinateCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationMFCoordinateGeneratedCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationMFGeneratedCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationMFManuscriptCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationMFRepresentationCore import GroupApproximation.Manuscript.OneSidedMFRadical.TensorSynchronizationTraceCore import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUniversalInstances import GroupApproximation.Analysis.AsymptoticModelMFEmbedding import GroupApproximation.Analysis.BlackadarKirchbergConvexSupportDensity import GroupApproximation.Analysis.BlackadarKirchbergCoordinateSelection import GroupApproximation.Analysis.MatrixCoronaAmplificationEquivAudit import GroupApproximation.Analysis.UniversalCStarAmalgamLarge import GroupApproximation.Computability.BenignSupCodeModelSemantics import GroupApproximation.Endpoint.MFRecognitionFiniteCertificatesAudit import GroupApproximation.GroupTheory.HNNFiniteQuotientCriterion import GroupApproximation.Higman.BenignJoinFiniteQuotientMap import GroupApproximation.Higman.CentralHNNFiniteQuotientMap import GroupApproximation.Higman.CodedTransportStarProfinite import GroupApproximation.Higman.ConjugatorGraphProfinite import GroupApproximation.Higman.FreeGroupHall import GroupApproximation.Higman.FreeLampFiniteBaseProfinite import GroupApproximation.Higman.FreeLampProfiniteEmbedding import GroupApproximation.Higman.HNNSubextensionFiniteBaseProfinite import GroupApproximation.Higman.MatchedSubgroupAmalgamWordReflection import GroupApproximation.Higman.OmegaHalfLineAscendingCriterion import GroupApproximation.Higman.OmegaHalfLineFiniteCutter import GroupApproximation.Higman.OmegaHalfLineFiniteHNN import GroupApproximation.Higman.OmegaHalfLineGraphGate import GroupApproximation.Higman.OmegaHalfLineLabelShift import GroupApproximation.Higman.OmegaHalfLineMatchedFiniteCutter import GroupApproximation.Higman.OmegaHalfLineReduction import GroupApproximation.Higman.OmegaHalfLineRightInsertion import GroupApproximation.Higman.OmegaHalfLineSemanticGraphWitness import GroupApproximation.Higman.OmegaHalfLineTargetCutter import GroupApproximation.Higman.PairedReturnCutterCentralHNN import GroupApproximation.Higman.PairedReturnImageIntersectionRefinement import GroupApproximation.Higman.PairedReturnLeftProduct import GroupApproximation.Higman.PairedReturnLeftProductProfinite import GroupApproximation.Higman.PairedReturnMatchedCutterProfinite import GroupApproximation.Higman.PairedReturnProfiniteWitness import GroupApproximation.Higman.PairedReturnQProfinite import GroupApproximation.Higman.ProfiniteBenignFactorizationReflection import GroupApproximation.Higman.ProfiniteBenignInfProductSeparable import GroupApproximation.Higman.ProfiniteBenignProductSeparable import GroupApproximation.Higman.ProfiniteCofinalClosedImage import GroupApproximation.Higman.TransportStarProdBotProfinite import GroupApproximation.Higman.TransportStarSourceProductSeparable import GroupApproximation.Manuscript.MFRecognition.ConcreteQCodeFamily import GroupApproximation.Manuscript.MFRecognition.FinitelyGeneratedNonMFQuotientAudit import GroupApproximation.Manuscript.MFRecognition.FixedUniversalFamily import GroupApproximation.Manuscript.MFRecognition.FixedUniversalFamilyRecursive import GroupApproximation.Manuscript.MFRecognition.FixedUniversalHostCompiler import GroupApproximation.Manuscript.MFRecognition.FixedUniversalHostOfOmega import GroupApproximation.Manuscript.MFRecognition.TwoSidedBridgeRelatorCode import GroupApproximation.Manuscript.MFRecognition.TwoSidedConcreteQCodeFamily import GroupApproximation.Sofic.ProfiniteFiniteExtensionLERF import GroupApproximation.Computability.BenignSupCodeSemantics import GroupApproximation.Analysis.CStarMatrixTwoByTwo import GroupApproximation.Analysis.RepresentedRootPlaneSpectralQuasiInvariant import GroupApproximation.Computability.BenignSupCodeSubgroupSemantics import GroupApproximation.Computability.ParametricRecursiveSwitchPresentation import GroupApproximation.GGT.HyperbolicTreeMetric import GroupApproximation.GGT.HyperbolicAdditiveTransfer import GroupApproximation.GGT.HyperbolicFreeGroupAH import GroupApproximation.GGT.HyperbolicTreeAction import GroupApproximation.GGT.HyperbolicWPDTransfer import GroupApproximation.GGT.HyperbolicTreeSegmentShift import GroupApproximation.GGT.BassSerreHNNLength import GroupApproximation.GGT.BassSerreHNNTree import GroupApproximation.GGT.BassSerreHNNIsTree import GroupApproximation.GGT.BassSerreHNNAction import GroupApproximation.GGT.BassSerreDoubleHNN import GroupApproximation.GGT.BassSerreHNNWPDInput import GroupApproximation.GGT.BassSerreHNNAxisWPD import GroupApproximation.GGT.TreeWPDAxis import GroupApproximation.GGT.CayleyGeodesicModel import GroupApproximation.GGT.CayleyGeodesicRealisation import GroupApproximation.GGT.ElementaryBowditch import GroupApproximation.GGT.ElementaryCentralizerAxis import GroupApproximation.GGT.ElementaryClosure import GroupApproximation.GGT.ElementaryCommonPower import GroupApproximation.GGT.ElementaryFillCentralizer import GroupApproximation.GGT.ElementaryFillConjugate import GroupApproximation.GGT.ElementaryMorse import GroupApproximation.GGT.ElementaryMorseChord import GroupApproximation.GGT.ElementaryMorseOrbit import GroupApproximation.GGT.ElementaryIndependence import GroupApproximation.GGT.ElementaryBowditchProof import GroupApproximation.GGT.ElementaryOsinNormalClosed import GroupApproximation.GGT.ElementaryMorseAlphabet import GroupApproximation.GGT.ElementaryMorseBiInfinite import GroupApproximation.GGT.ElementaryHypEmbedded import GroupApproximation.GGT.ElementaryProjectionCriterion import GroupApproximation.GGT.ElementaryProperFromTransversal import GroupApproximation.GGT.ElementaryOsinSNormal import GroupApproximation.GGT.ElementaryProperClosure import GroupApproximation.GGT.ElementaryTransfer import GroupApproximation.GGT.HullSC import GroupApproximation.GGT.HullSCCommonQuotient import GroupApproximation.GGT.HullSCCommonQuotientCorrected import GroupApproximation.GGT.HullSCConeOff import GroupApproximation.GGT.HullSCConeOffSpace import GroupApproximation.GGT.HullSCFilling import GroupApproximation.GGT.HullSCInjectivityTransfer import GroupApproximation.GGT.HullSCFreeProductFactor import GroupApproximation.GGT.HullSCHypEmbedded import GroupApproximation.GGT.HullSCRelatorFamily import GroupApproximation.GGT.HullSCRelatorWord import GroupApproximation.GGT.HullSCRotatingFamily import GroupApproximation.GGT.HullSCDGO import GroupApproximation.GGT.HullSCSmallCancellation import GroupApproximation.GGT.HullSCTheorem51 import GroupApproximation.GGT.KazhdanHyp import GroupApproximation.GGT.KazhdanHypGirthEight import GroupApproximation.GGT.KazhdanHypLinkGap import GroupApproximation.GGT.KazhdanHypPolygonal import GroupApproximation.GGT.KazhdanHypQuadrangle import GroupApproximation.GGT.KazhdanHypQuadrangleBridge import GroupApproximation.GGT.KazhdanHypTable import GroupApproximation.GGT.KazhdanHypTorsionCriterion import GroupApproximation.GGT.RelHypDefinition import GroupApproximation.GGT.PingPongFreeSubgroup import GroupApproximation.GGT.RelHypLetterPieces import GroupApproximation.GGT.RelHypAbelianPartnerNoGo import GroupApproximation.GGT.RelHypOsinTheorem24Repaired import GroupApproximation.GGT.PingPongReduction import GroupApproximation.GGT.RelHypElementaryAmenable import GroupApproximation.GGT.RelHypFournierFacio import GroupApproximation.GGT.RelHypFreeProductPeripheral import GroupApproximation.GGT.RelHypKazhdanNonElementary import GroupApproximation.GGT.RelHypOsinTheorem24 import GroupApproximation.GGT.RelHypOsinTheorem24Refuted import GroupApproximation.GGT.CayleyFourPointBridge import GroupApproximation.GGT.RelHypRelativeCayley import GroupApproximation.GGT.RelHypWithoutKazhdan import GroupApproximation.GGT.WPDAcylindricalHyperbolicity import GroupApproximation.GGT.WPDDGOReduction import GroupApproximation.GGT.WPDElement import GroupApproximation.GGT.WPDHyperbolicallyEmbedded import GroupApproximation.GGT.WPDMinasyanOsinSkeleton import GroupApproximation.GGT.WPDElementaryEmbedding import GroupApproximation.GGT.OsinComponents import GroupApproximation.GGT.OsinEnlargement import GroupApproximation.GGT.OsinSeparatingCosets import GroupApproximation.GGT.OsinPenetration import GroupApproximation.GGT.OsinGeodesicWord import GroupApproximation.Higman.OmegaFillLinkPreimage import GroupApproximation.Higman.OmegaFatSlimCanonicalOne import GroupApproximation.Higman.OmegaFatSlimCanonicalTwo import GroupApproximation.Higman.OmegaFatSlimCanonicalThree import GroupApproximation.Manuscript.NonMF.HullFillOsinNormalReduction import GroupApproximation.Analysis.NormCoronaAsymptoticLiftRestriction import GroupApproximation.GGT.HullSCUnionGeometryNormalForm import GroupApproximation.Higman.OmegaTowerSelectedRowWord import GroupApproximation.Higman.OmegaTowerSelectedAbstractEndpointFactors import GroupApproximation.GGT.HullSCUnionGeometryFourPoint import GroupApproximation.Higman.OmegaFatShearedLinkSemantic import GroupApproximation.Higman.OmegaFatShearedLinkBase import GroupApproximation.Higman.OmegaFatLinkEmbeddingObstruction import GroupApproximation.Higman.OmegaTowerSelectedArbitraryReturnWitness import GroupApproximation.Analysis.ShulmanFillNormingCoronaRoute import GroupApproximation.Analysis.ShulmanFillNormingAmalgamWitness import GroupApproximation.Analysis.ShulmanFillNormingAsymptotic import GroupApproximation.Analysis.ShulmanFillNormingPrefixBlock import GroupApproximation.Analysis.ShulmanFillNormingFactorImages import GroupApproximation.Analysis.ShulmanFillNormingFamily import GroupApproximation.Analysis.ShulmanFillNormingResiduallyFinite import GroupApproximation.Higman.OmegaTowerSelectedArbitraryTargetClassifier import GroupApproximation.GGT.CayleyGeodesicQuotient import GroupApproximation.Higman.OmegaFillLeadLinkBenign import GroupApproximation.Analysis.ShulmanFillNormingAsymptoticMF import GroupApproximation.Analysis.ShulmanFillNormingBlockHilbert import GroupApproximation.Analysis.ShulmanFillNormingConjugation import GroupApproximation.Analysis.ShulmanFillNormingDCStar import GroupApproximation.GGT.OsinTheorem54Lemma24 import GroupApproximation.GGT.OsinLemma512Torsion import GroupApproximation.GGT.HullSCRelatorSeparationBall import GroupApproximation.GGT.HullSCRelatorSeparationGaps import GroupApproximation.GGT.HullSCRelatorSeparationBlock import GroupApproximation.GGT.OsinTheorem54SeparatingCosets import GroupApproximation.GGT.OsinTheorem54SepReversal import GroupApproximation.GGT.OsinTheorem54SepComponents import GroupApproximation.GGT.HullSCRelatorSeparationValues import GroupApproximation.GGT.HullSCRelatorSeparationRefuted import GroupApproximation.GGT.HullSCRelatorSeparationRepair import GroupApproximation.GGT.OsinTheorem54SepRuns import GroupApproximation.GGT.HullSCUnionGeometryCoprod import GroupApproximation.GGT.HullSCUnionGeometryAcylindrical import GroupApproximation.GGT.HullSCUnionGeometryConcat import GroupApproximation.GGT.HullSCUnionGeometryCrossing import GroupApproximation.GGT.HullSCUnionGeometryLineal import GroupApproximation.GGT.HullSCUnionGeometryPrefix import GroupApproximation.GGT.HullSCUnionGeometryElliptic import GroupApproximation.GGT.HullSCUnionGeometryLongSyllable import GroupApproximation.GGT.HullSCUnionGeometryFactorBranch import GroupApproximation.GGT.HullSCUnionGeometryCyclic import GroupApproximation.GGT.HullSCUnionGeometryTrichotomy import GroupApproximation.GGT.HullSCUnionGeometryHyperbolicFactor import GroupApproximation.GGT.OsinTheorem54SepTransport import GroupApproximation.GGT.OsinTheorem54SepSplit import GroupApproximation.GGT.OsinTheorem54SepFinite import GroupApproximation.GGT.OsinTheorem54SepSymmetric import GroupApproximation.GGT.HullSCRelatorSeparationLetters import GroupApproximation.GGT.OsinTheorem54SepPolygon import GroupApproximation.GGT.OsinTheorem54SepCommRefuted import GroupApproximation.GGT.HullSCRelatorSeparationComponent import GroupApproximation.GGT.HullSCRelatorSeparationSpacing import GroupApproximation.GGT.HullSCRelatorSeparationConnector import GroupApproximation.GGT.HullSCRelatorSeparationNotQG import GroupApproximation.GGT.HullSCRelatorSeparationRotation import GroupApproximation.Analysis.ShulmanFillNormingBlockHom import GroupApproximation.Analysis.ShulmanFillNormingCoronaMap import GroupApproximation.Analysis.ShulmanFillNormingSeqHom import GroupApproximation.Analysis.ShulmanFillNormingProductMF import GroupApproximation.GGT.HullSCRelatorSeparation2Word import GroupApproximation.GGT.HullSCRelatorSeparation2Component import GroupApproximation.GGT.HullSCRelatorSeparation2Gaps import GroupApproximation.GGT.HullSCRelatorSeparation2Design import GroupApproximation.GGT.HullSCRelatorSeparation2Rigid import GroupApproximation.GGT.HullSCRelatorSeparation2Core import GroupApproximation.GGT.HullSCRelatorSeparation2Statement import GroupApproximation.GGT.HullSCUnionGeometrySyllableSplit import GroupApproximation.GGT.HullSCUnionGeometryWitness import GroupApproximation.GGT.HullSCUnionGeometryVirtuallyCyclic import GroupApproximation.Analysis.ShulmanFillNormingConjugationLift import GroupApproximation.GGT.HullSCRelatorSeparation2QuasiGeodesic import GroupApproximation.GGT.HullSCRelatorSeparation2Theorem51 import GroupApproximation.GGT.HullSCRelatorSeparation2ConeOff import GroupApproximation.GGT.HullSCUnionGeometrySyllableCount import GroupApproximation.Analysis.ShulmanFillNormingBlockLimit import GroupApproximation.Analysis.ShulmanFillNormingGluing import GroupApproximation.Analysis.ShulmanFillNormingMatrixFlatten import GroupApproximation.GGT.OsinTheorem54SepTransportFam import GroupApproximation.GGT.OsinTheorem54SepFiniteFam import GroupApproximation.GGT.OsinTheorem54SepSymmetricFam import GroupApproximation.GGT.OsinTheorem54Family import GroupApproximation.GGT.HullSCRelatorSeparation2ConeOffSpace import GroupApproximation.GGT.HullSCRelatorSeparation2RotatingFamily import GroupApproximation.GGT.HullSCUnionGeometryFactorDichotomy import GroupApproximation.GGT.HullSCUnionGeometryBranchPoint import GroupApproximation.GGT.HullSCUnionGeometryFactorInput import GroupApproximation.GGT.HullSCUnionGeometryShortBranch import GroupApproximation.GGT.HullSCUnionGeometryAssembly import GroupApproximation.Analysis.ShulmanFillNormingDoubleMF import GroupApproximation.GGT.HullSCRelatorSeparation2Filling import GroupApproximation.Analysis.ShulmanFillNormingDoubledData import GroupApproximation.Analysis.BlackadarKirchbergAbstractFiniteDimensionalLift import GroupApproximation.Analysis.BlackadarKirchbergFiniteCoordinateUCP import GroupApproximation.Analysis.BlackadarKirchbergFiniteCoordinateLinearFactorization import GroupApproximation.Analysis.BlackadarKirchbergMFUCPApproximateInverse import GroupApproximation.Analysis.MFAlgebraAmalgamFaithfulEval import GroupApproximation.Analysis.MFAlgebraHNNPermanence import GroupApproximation.Analysis.ShulmanCoronaContractionRepresentative import GroupApproximation.Analysis.ShulmanCoronaBoundedRepresentative import GroupApproximation.Analysis.ShulmanContractiveAsymptoticLift import GroupApproximation.Analysis.ShulmanCoronaHalmosCommutator import GroupApproximation.Analysis.ShulmanCoronaHalmosSequence import GroupApproximation.Analysis.ShulmanDenseCompatibility import GroupApproximation.Analysis.ShulmanDiagonalSelection import GroupApproximation.Analysis.ShulmanUnitaryConjugationControl import GroupApproximation.Analysis.ShulmanDiagonalConjugation import GroupApproximation.Analysis.UniversalCStarAmalgamCoordinate import GroupApproximation.Computability.FreeEdgeTowerExactEdgeData import GroupApproximation.Computability.FreeEdgeTowerExactEdgeHom import GroupApproximation.Computability.FreeEdgeTowerExactEdge import GroupApproximation.Computability.FreeEdgeTowerExactIterationCore import GroupApproximation.Computability.FreeEdgeTowerExactIteration import GroupApproximation.Computability.FreeEdgeTowerMarkedCompiler import GroupApproximation.Higman.CodedBenignWitness import GroupApproximation.Higman.TransportStarCodeSemantics import GroupApproximation.Higman.OmegaFiniteTower import GroupApproximation.Higman.OmegaTowerBlockWindow import GroupApproximation.Higman.OmegaTowerPinchRewrite import GroupApproximation.Higman.OmegaTowerRightLabelInverseCanonical import GroupApproximation.Higman.PairedReturnFiveCutterProfiniteReduction import GroupApproximation.Higman.ReifiedHigmanWitnessAgreeCode import GroupApproximation.Higman.ReifiedHigmanWitnessAgreeConstants import GroupApproximation.Higman.ReifiedPrimitiveRecursiveProgram import GroupApproximation.Higman.ReifiedPrimitiveRecursiveCode import GroupApproximation.Higman.ReifiedPrimitiveRecursiveTowerBase import GroupApproximation.Higman.ReifiedHigmanWitnessBaseCode import GroupApproximation.Higman.ReifiedHigmanWitnessRhoCode import GroupApproximation.Higman.ReifiedHigmanWitnessSigmaCode import GroupApproximation.Higman.ReifiedHigmanWitnessThetaCode import GroupApproximation.Higman.TransportStarSpecialJoinClosed import GroupApproximation.Manuscript.MFRecognition.HNNTraceEdgeDensity import GroupApproximation.Manuscript.MFRecognition.HNNTraceCovarianceGenerator import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCornerConcrete import GroupApproximation.Manuscript.MFRecognition.PrintedTarskiCertificateDerivation import GroupApproximation.Manuscript.MFRecognition.PrintedTarskiCertificateSyntax import GroupApproximation.Manuscript.MFRecognition.PrintedTarskiCertificateDecision import GroupApproximation.Manuscript.MFRecognition.PrintedTarskiCertificate import GroupApproximation.GGT.RelHypOsin24CayleyLeaf import GroupApproximation.GGT.RelHypOsin24CayleyEndpoint import GroupApproximation.GGT.OsinTheorem54SepPolygonVertex import GroupApproximation.GGT.RelHypOsin24CollapseModel import GroupApproximation.GGT.OsinTheorem54SepFourGon import GroupApproximation.GGT.OsinTheorem54SepFourGonSide import GroupApproximation.Analysis.ShulmanFillNormingDoubledFlip import GroupApproximation.Sofic.Osin24FoldWitnessLegality import GroupApproximation.GGT.DGOCorollary612Malnormal import GroupApproximation.GGT.HullSCRelatorSeparation2FillingData import GroupApproximation.GGT.HullSCRelatorSeparation2Assembly import GroupApproximation.GGT.HullSCRelatorSeparation2Quotient import GroupApproximation.GGT.HullSCRelatorSeparation2ListFacts import GroupApproximation.GGT.HullSCRelatorSeparation2Rotation import GroupApproximation.Sofic.Osin24FactorEdgeBound import GroupApproximation.GGT.OsinTheorem54SepFourGonCorner import GroupApproximation.GGT.RelHypOsin24Collapse import GroupApproximation.GGT.HullSCRelatorSeparation2Mirror import GroupApproximation.GGT.HullSCRelatorSeparation2MirrorRun import GroupApproximation.Higman.OmegaFatShearedCoordinateEdge import GroupApproximation.GGT.DGOIsolatedComponentWitness import GroupApproximation.GGT.DGOIsolatedComponentCoset import GroupApproximation.GGT.RelHypOsin24CayleyWitness import GroupApproximation.GGT.HullSCRelatorSeparation2Locate import GroupApproximation.GGT.OsinTheorem54SepSmul import GroupApproximation.Analysis.BlackadarKirchbergScalarCoordinateStateDensity import GroupApproximation.Sofic.Osin24FoldedWalk import GroupApproximation.GGT.OsinTheorem54SepFourGonGeneral import GroupApproximation.GGT.OsinTheorem54SepFourGonPinning import GroupApproximation.GGT.OsinTheorem54SepCommIndex import GroupApproximation.GGT.HullSCRelatorSeparation2MirrorGap import GroupApproximation.GGT.HullSCRelatorSeparation2Aligned import GroupApproximation.Analysis.ShulmanFillNormingEllTwoModels import GroupApproximation.GGT.HullSCRelatorSeparation2MixedCase import GroupApproximation.GGT.DGOIsolatedComponentBridge import GroupApproximation.Analysis.ShulmanFillNormingScalarMF import GroupApproximation.Analysis.ShulmanFillNormingTheorem4Refuted import GroupApproximation.GGT.OsinTheorem54SepFourGonQuasi import GroupApproximation.Higman.CodedTransportStarRankThree import GroupApproximation.GGT.HyperbolicThinTriangles import GroupApproximation.GGT.DGOIsolatedComponentReduce import GroupApproximation.GGT.HullSCRelatorSeparation2Cross import GroupApproximation.GGT.OsinTheorem54SepFourGonInterface import GroupApproximation.GGT.HullSCRelatorSeparation2Centralizer import GroupApproximation.GGT.HullSCRelatorSeparation2Power import GroupApproximation.GGT.OsinTheorem54SepCommSet import GroupApproximation.GGT.DGOIsolatedComponentTransport import GroupApproximation.GGT.OsinTheorem54SepFourGonMeet import GroupApproximation.GGT.HullSCRelatorSeparation2Diagonal import GroupApproximation.Manuscript.MFRecognition.PositiveBranchResidualFiniteness import GroupApproximation.Higman.OmegaFatShearedCoordinateBase import GroupApproximation.Higman.OmegaFatShearedCoordinateShift import GroupApproximation.GGT.HullSCRelatorSeparation2Aperiodic import GroupApproximation.Higman.OmegaFatShearedFirstCoordinateMatched import GroupApproximation.GGT.OsinTheorem54SepElementaryBall import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCompatibleCorner import GroupApproximation.Manuscript.MFRecognition.HNNPermanenceUedaCoordinateCorner import GroupApproximation.GGT.OsinTheorem54SepLemma55 import GroupApproximation.GGT.OsinTheorem54SepLetterCount import GroupApproximation.Higman.OmegaFatShearedFirstSemanticMatched import GroupApproximation.GGT.OsinTheorem54SepOrder import GroupApproximation.GGT.OsinTheorem54SepSubGeodesic import GroupApproximation.GGT.HullSCRelatorSeparation2Diff import GroupApproximation.GGT.HullSCRelatorSeparation2PowFam import GroupApproximation.GGT.HullSCRelatorSeparation2Join import GroupApproximation.GGT.OsinTheorem54SepSegmentComp import GroupApproximation.GGT.HullSCRelatorSeparation2Tails import GroupApproximation.GGT.HullSCRelatorSeparation2Window import GroupApproximation.GGT.OsinTheorem54SepBlockConj import GroupApproximation.Analysis.ShulmanFillNormingExistentialLift import GroupApproximation.GGT.HullSCRelatorSeparation2AlignedClose import GroupApproximation.GGT.DGOThinPolygonVertex import GroupApproximation.GGT.OsinTheorem54SepSegmentVertex import GroupApproximation.GGT.OsinTheorem54SepLemma59 import GroupApproximation.GGT.HullSCRelatorSeparation2Segment import GroupApproximation.GGT.HullSCRelatorSeparation2MirrorClose import GroupApproximation.GGT.OsinTheorem54SepEnum import GroupApproximation.GGT.OsinTheorem54SepGapY import GroupApproximation.GGT.HullSCRelatorSeparation2Assemble import GroupApproximation.GGT.DGOPolygonGeodesicChain import GroupApproximation.GGT.HullSCRelatorSeparation2NoCommute import GroupApproximation.GGT.HullSCRelatorSeparation2Ledger import GroupApproximation.GGT.OsinTheorem54SepInhabit import GroupApproximation.GGT.DGOShortIsolatingCycle import GroupApproximation.Analysis.ShulmanFillNormingExistentialLiftDouble import GroupApproximation.Analysis.ShulmanFillNormingExistentialLiftFlip import GroupApproximation.Analysis.ShulmanFillNormingExistentialLiftPair import GroupApproximation.Analysis.ShulmanFillNormingExistentialLiftTwoLeg import GroupApproximation.GGT.OsinTheorem54SepRigidityReduction import GroupApproximation.GGT.OsinTheorem54SepRigidityTrivial import GroupApproximation.Analysis.ShulmanFillNormingExistentialLiftFaithful import GroupApproximation.GGT.DGOCycleSplice import GroupApproximation.GGT.DGOCycleAssembly import GroupApproximation.GGT.OsinTheorem54SepDistBase import GroupApproximation.GGT.DGOIsolatedComponentVertexDist import GroupApproximation.GGT.DGOIsolatedComponentRecut import GroupApproximation.GGT.DGOIsolatedComponentSplit import GroupApproximation.GGT.HullSCRelatorSeparation2Rigidity import GroupApproximation.Analysis.ShulmanFillNormingEllTwoTheorem10 import GroupApproximation.GGT.DGOIsolatedComponentNormalise import GroupApproximation.Analysis.ShulmanFillNormingExistentialLiftPrinted import GroupApproximation.GGT.DGOFourGonThin import GroupApproximation.GGT.DGOShortCycleIndices import GroupApproximation.GGT.OsinTheorem54SepDistPrefix import GroupApproximation.GGT.OsinTheorem54SepDistSuffix import GroupApproximation.GGT.DGOIsolatedComponentCut import GroupApproximation.Analysis.ShulmanFillNormingFactorMapComp import GroupApproximation.GGT.DGOTwoConnectorSplice import GroupApproximation.GGT.OsinTheorem54SepDistStep import GroupApproximation.GGT.DGOIsolatedComponentStraddle import GroupApproximation.GGT.OsinTheorem54SepDistLeSep import GroupApproximation.GGT.OsinTheorem54SepLetterMult import GroupApproximation.GGT.OsinTheorem54SepAssemble import GroupApproximation.GGT.DGOIsolatedComponentRotate import GroupApproximation.Analysis.ShulmanFillNormingFactorMapRange import GroupApproximation.Analysis.ShulmanFillNormingRecognitionWiring import GroupApproximation.GGT.OsinTheorem54SepLemma510Right import GroupApproximation.GGT.OsinTheorem54SepAssembleFull import GroupApproximation.GGT.DGOIsolatedComponentRotateCut import GroupApproximation.GGT.DGOIsolatedComponentCollapseCut import GroupApproximation.GGT.DGOIsolatedComponentSideForm import GroupApproximation.GGT.OsinTheorem54SepFourGonOpposite import GroupApproximation.GGT.OsinTheorem54SepDeepSixForm import GroupApproximation.Analysis.CStarSeparableFaithfulRepresentation import GroupApproximation.Analysis.CStarHilbertTransport import GroupApproximation.GGT.HullSCRelatorSeparation2Ball import GroupApproximation.GGT.HullSCRelatorSeparation2MirrorBall import GroupApproximation.Analysis.CStarHilbertCountableBasis import GroupApproximation.GGT.OsinTheorem54SepRotatePolygon import GroupApproximation.GGT.HullSCRelatorSeparation2Span import GroupApproximation.GGT.DGOReversedSplice import GroupApproximation.GGT.DGOShortIsolatingCycleMain import GroupApproximation.GGT.DGOIsolatedComponentBoundFourGon import GroupApproximation.GGT.OsinTheorem54SepFourGonPolygon import GroupApproximation.GGT.OsinTheorem54SepRotateComponent import GroupApproximation.GGT.OsinTheorem54SepTwoBlockRot import GroupApproximation.GGT.HullSCRelatorSeparation2Extract import GroupApproximation.Analysis.CStarSeparableTypeZeroRepresentation import GroupApproximation.GGT.HullSCRelatorSeparation2OtherArc import GroupApproximation.GGT.DGOIsolatedComponentSideZero import GroupApproximation.GGT.DGOGeodesicChainComponents import GroupApproximation.GGT.DGOSafeBlock import GroupApproximation.GGT.DGOPolygonJoin import GroupApproximation.GGT.DGOPolygonCutFourGon import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyNamed import GroupApproximation.GGT.HullSCRelatorSeparation2Apply import GroupApproximation.GGT.DGOPolygonFarGon import GroupApproximation.Analysis.ShulmanFillNormingTailAsymptotic import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyComp import GroupApproximation.Analysis.ShulmanFillNormingTailAsymptoticMF import GroupApproximation.Analysis.ShulmanFillNormingTailPrinted import GroupApproximation.Analysis.ShulmanFillNormingPrintedPairRefuted import GroupApproximation.Analysis.ShulmanFillNormingPrintedPairCharacter import GroupApproximation.GGT.DGOPolygonEdgeGon import GroupApproximation.GGT.DGOPolygonLemma417 import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyBlock import GroupApproximation.GGT.HullSCRelatorSeparation2ApplySpelling import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyGap import GroupApproximation.GGT.DGOPolygonBaseCaseTower import GroupApproximation.Analysis.ShulmanFillNormingTailTruncation import GroupApproximation.Analysis.ShulmanFillNormingTailPair import GroupApproximation.GGT.HullSCRelatorSeparation2ApplySide import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyPair import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyClose import GroupApproximation.Analysis.ShulmanFillNormingTailCorner import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyRotate import GroupApproximation.Analysis.ShulmanFillNormingTailShift import GroupApproximation.Analysis.ShulmanFillNormingTailShiftLimit import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyPin import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyAssemble import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyDispatch import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyExp import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyMatch import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyMixed import GroupApproximation.Analysis.ShulmanFillNormingTailSeqHom import GroupApproximation.Analysis.ShulmanFillNormingTailGlueAlign import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyMixedClose import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyMixedInv import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyNarrow import GroupApproximation.Analysis.ShulmanFillNormingTailGluing import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyNarrowGap import GroupApproximation.Analysis.ShulmanFillNormingTailDoubleMF import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyNarrowPair import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyPiece import GroupApproximation.Analysis.ShulmanFillNormingTailPrintedPair import GroupApproximation.Analysis.ShulmanFillNormingTailRecognition import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyIface import GroupApproximation.Analysis.CStarInfiniteDimensionalGNS import GroupApproximation.Analysis.CStarInfiniteFaithfulRepresentation import GroupApproximation.Analysis.ShulmanFillNormingTailRoute import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyTwoBlock import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyFourWay import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyShortSide import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyLoxGap import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyCompose import GroupApproximation.GGT.HullSCRelatorSeparation2ApplyQuantified /-! # An unconditional construction of a finitely presented nonsofic group This library proves that a nonsofic group exists, and that a finitely presented one does. Both are closed theorems: neither takes a hypothesis standing in for a construction, and neither is a parameterized implication advertised as an existence result. **Start at `GroupApproximation.Public`.** It is the reading path -- the declarations a referee needs, each named against the theorem it establishes. The statement-by-statement correspondence between this construction and its manuscript is `notes/CLAIM_MAP.md`, generated from the paper's own margin notes; the manuscript itself is no longer kept in the repository. The two manuscripts here are `property_tt_leavitt.tex`, on coordinate-block factorization and `(TT)/T`, and `non_mf_groups_exist.tex`, on operator-norm matrix approximation; neither states the nonsofic theorems. ## What is proved here rather than assumed Every theorem the paper cites for its own proofs is proved in this library, in the exact form used, so each is an input to the manuscript and not to the development: Kun's expander decomposition (`KunDecomposition`), the Kun--Thom centralizer obstruction (`KunThomTheorem`), Shalom's finitely presented Kazhdan covers (`ShalomFinitePresentation`), and property `(T)` for elementary groups over finite-type algebras over finite fields (`FiniteFieldElementaryPropertyT`, with the explicit Kazhdan pair of `FreeElementaryPropertyT`). The Ershov--Jaikin-Zapirain theorem over an arbitrary finitely generated ring is not formalized, and nothing here needs it. The `K₁`-theoretic input is likewise eliminated: `BinaryLeavitt.K1_trivial` proves `K₁(L_k(1,2)) = 0` in Whitehead form by an elementary two-exit elimination, so the localization-sequence citation is confirmation rather than dependency. ## The construction The coefficient ring is the actual universal binary Leavitt algebra, defined as the presented quotient of the free algebra; its stream-operator representation proves that quotient nontrivial, so no faithfulness claim is needed. `UniversalRankFour.compressionSetup` constructs the algebraic setup rather than accepting it from a caller, and the corner subgroup carrying the non-LEF obstruction is identified with Thompson's group `V` (`ThompsonVWitness.thompsonV_not_isLEF`), proved non-LEF unconditionally with no Higman presentation input. `MainResults.universalLeavittEL4_not_isSofic` supplies the initial nonsofic group; `TableCover` builds its finitely presented cover, and `KazhdanCover` the Kazhdan one. ## Trust surface `GroupApproximation.Audit` prints the dependency report for the public results on an ordinary build. `scripts/Audit.lean` independently walks the transitive dependency closure of the whole namespace and fails on anything beyond `propext`, `Classical.choice`, and `Quot.sound`; `scripts/check.py` scans the source text for what the kernel cannot see, including files that are never compiled. -/