import OAI.MathematicalPhysics.Boltzmann.Model import OAI.MathematicalPhysics.Boltzmann.Admissibility import OAI.MathematicalPhysics.Boltzmann.Branching.RenormalizationBounds import OAI.MathematicalPhysics.Boltzmann.Branching.AdmissibleDatumCongruence import OAI.MathematicalPhysics.Boltzmann.Branching.Moments import OAI.MathematicalPhysics.Boltzmann.Approximation.ColoredDifferenceAlgebra import OAI.MathematicalPhysics.Boltzmann.Collision.AxialFlow import OAI.MathematicalPhysics.Boltzmann.Collision.AnalyticTools import OAI.MathematicalPhysics.Boltzmann.Branching.FanNullSet import OAI.MathematicalPhysics.Boltzmann.Branching.VolterraFubini import OAI.MathematicalPhysics.Boltzmann.Branching.TriangularLinearMap import OAI.MathematicalPhysics.Boltzmann.Branching.SquareIntegralToL1 import OAI.MathematicalPhysics.Boltzmann.Branching.SeparatedMeasureTail import OAI.MathematicalPhysics.Boltzmann.Branching.RightAverageBound import OAI.MathematicalPhysics.Boltzmann.Branching.RealL1ApproximationLimit import OAI.MathematicalPhysics.Boltzmann.Branching.PullbackRegularLimit import OAI.MathematicalPhysics.Boltzmann.Branching.SubmersionNullPreimage import OAI.MathematicalPhysics.Boltzmann.Branching.PullbackCoordinates import OAI.MathematicalPhysics.Boltzmann.Branching.PublishedInputs import OAI.MathematicalPhysics.Boltzmann.Branching.CausalConvolution import OAI.MathematicalPhysics.Boltzmann.Compactness.MeasurableResolvent import OAI.MathematicalPhysics.Boltzmann.Branching.TransportCutoff import OAI.MathematicalPhysics.Boltzmann.Branching.PairwiseSubsequenceCauchy import OAI.MathematicalPhysics.Boltzmann.Branching.MarginalUniformIntegrability import OAI.MathematicalPhysics.Boltzmann.Branching.LogarithmicIteration import OAI.MathematicalPhysics.Boltzmann.Branching.GrowthContradiction import OAI.MathematicalPhysics.Boltzmann.Branching.AlmostEverywhereGrowth import OAI.MathematicalPhysics.Boltzmann.Branching.DatumBounds import OAI.MathematicalPhysics.Boltzmann.Branching.CompactParameterConvergence import OAI.MathematicalPhysics.Boltzmann.Branching.SupportedTensorConvergence import OAI.MathematicalPhysics.Boltzmann.Collision.AngularPairTests import OAI.MathematicalPhysics.Boltzmann.Branching.LossIntegrability import OAI.MathematicalPhysics.Boltzmann.Collision.SphereAntipodal import OAI.MathematicalPhysics.Boltzmann.Branching.ReferenceCollisionGeometry import OAI.MathematicalPhysics.Boltzmann.Branching.ReferenceAngularCharts import OAI.MathematicalPhysics.Boltzmann.Branching.ReferenceMinorization import OAI.MathematicalPhysics.Boltzmann.Branching.ReferenceFlightLaws import OAI.MathematicalPhysics.Boltzmann.Branching.ReferenceBranchingHistories import OAI.MathematicalPhysics.Boltzmann.Branching.ReferenceHistoryMoments import OAI.MathematicalPhysics.Boltzmann.Branching.ReferenceGrowthBlocks import OAI.MathematicalPhysics.Boltzmann.Branching.PerturbedFiniteBlock import OAI.MathematicalPhysics.Boltzmann.Branching.OutgoingPairIntegral import OAI.MathematicalPhysics.Boltzmann.Branching.NormalReflectionGeometry import OAI.MathematicalPhysics.Boltzmann.Collision.SphereIsometryMeasure import OAI.MathematicalPhysics.Boltzmann.Collision.VelocityFourierMultiplier import OAI.MathematicalPhysics.Boltzmann.Branching.L2PairingBound import OAI.MathematicalPhysics.Boltzmann.Branching.SpacetimeFourierCoordinates import OAI.MathematicalPhysics.Boltzmann.Collision.FourierL2Identification import OAI.MathematicalPhysics.Boltzmann.Collision.VelocityWeight import OAI.MathematicalPhysics.Boltzmann.Collision.TransverseAverage import OAI.MathematicalPhysics.Boltzmann.Jets.JetProfiles import OAI.MathematicalPhysics.Boltzmann.Collision.AxialJointAnalytic import OAI.MathematicalPhysics.Boltzmann.Collision.GaussianFrequency import OAI.MathematicalPhysics.Boltzmann.Branching.StripeCells import OAI.MathematicalPhysics.Boltzmann.Branching.PlaneChart import OAI.MathematicalPhysics.Boltzmann.Jets.JetBarrierKinetic import OAI.MathematicalPhysics.Boltzmann.Branching.FiveGainRank import OAI.MathematicalPhysics.Boltzmann.Collision.MityaginPublished import OAI.MathematicalPhysics.Boltzmann.Collision.AnalyticRankAlmostEverywhere import OAI.MathematicalPhysics.Boltzmann.Collision.MityaginDischarge import OAI.MathematicalPhysics.Boltzmann.Branching.RedundantPlaneIntegral import OAI.MathematicalPhysics.Boltzmann.Collision.CarlemanNormalCoordinates import OAI.MathematicalPhysics.Boltzmann.Collision.WeightAlgebra import OAI.MathematicalPhysics.Boltzmann.Collision.CarlemanOperator import OAI.MathematicalPhysics.Boltzmann.Branching.GainNonnegative import OAI.MathematicalPhysics.Boltzmann.Collision.CollisionMeasure import OAI.MathematicalPhysics.Boltzmann.Compactness.KineticDensityMeasurable import OAI.MathematicalPhysics.Boltzmann.Collision.GaussianEstimates import OAI.MathematicalPhysics.Boltzmann.Approximation.RegularizedLogBounds import OAI.MathematicalPhysics.Boltzmann.Compactness.EntropyIntegralBalance import OAI.MathematicalPhysics.Boltzmann.Collision.ScalarEntropyConvex import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricSlice import OAI.MathematicalPhysics.Boltzmann.Collision.SheetGain import OAI.MathematicalPhysics.Boltzmann.Branching.ChartPointLift import OAI.MathematicalPhysics.Boltzmann.Compactness.UniformGain import OAI.MathematicalPhysics.Boltzmann.Collision.SheetIntervals import OAI.MathematicalPhysics.Boltzmann.Collision.AxialAtomicSheet import OAI.MathematicalPhysics.Boltzmann.Collision.SheetMixtures import OAI.MathematicalPhysics.Boltzmann.Branching.HotGainReduction import OAI.MathematicalPhysics.Boltzmann.Branching.PowerDiskMixture import OAI.MathematicalPhysics.Boltzmann.Branching.HotQuadraticGain import OAI.MathematicalPhysics.Boltzmann.Branching.MixedRealGain import OAI.MathematicalPhysics.Boltzmann.Branching.RegularChart import OAI.MathematicalPhysics.Boltzmann.Branching.AxisInput import OAI.MathematicalPhysics.Boltzmann.Branching.MismatchSlices import OAI.MathematicalPhysics.Boltzmann.Branching.AxisMismatch import OAI.MathematicalPhysics.Boltzmann.Branching.AffineSlices import OAI.MathematicalPhysics.Boltzmann.Branching.SlopedChart import OAI.MathematicalPhysics.Boltzmann.Branching.LargeOutput import OAI.MathematicalPhysics.Boltzmann.Branching.WidthTails import OAI.MathematicalPhysics.Boltzmann.Jets.JetBarriers import OAI.MathematicalPhysics.Boltzmann.Jets.TorusChart import OAI.MathematicalPhysics.Boltzmann.Jets.JetPeriodicDatum import OAI.MathematicalPhysics.Boltzmann.Jets.JetSupersolutions import OAI.MathematicalPhysics.Boltzmann.Jets.JetEnvelopeTimeIntegral import OAI.MathematicalPhysics.Boltzmann.Branching.CompressedAxialDecay import OAI.MathematicalPhysics.Boltzmann.Branching.ExtendedProductionScale import OAI.MathematicalPhysics.Boltzmann.Branching.NonnegativeGainCongruence import OAI.MathematicalPhysics.Boltzmann.Branching.InverseFourierL2 import OAI.MathematicalPhysics.Boltzmann.Branching.HistoryWeightNormalization import OAI.MathematicalPhysics.Boltzmann.Branching.SmoothTestFamily import OAI.MathematicalPhysics.Boltzmann.Branching.AeWindowPatching import OAI.MathematicalPhysics.Boltzmann.Jets.AnnularEnvelopes import OAI.MathematicalPhysics.Boltzmann.Jets.TorusAnnularIntegrability import OAI.MathematicalPhysics.Boltzmann.Branching.CommonMomentEnvelope import OAI.MathematicalPhysics.Boltzmann.Jets.TorusTailRegions import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakL1Operations import OAI.MathematicalPhysics.Boltzmann.Branching.AverageMajorant import OAI.MathematicalPhysics.Boltzmann.Branching.InMeasureDifference import OAI.MathematicalPhysics.Boltzmann.Branching.VanishingMajorant import OAI.MathematicalPhysics.Boltzmann.Branching.VaryingBoundedMultiplier import OAI.MathematicalPhysics.Boltzmann.Collision.WeightLocalL1 import OAI.MathematicalPhysics.Boltzmann.Compactness.UniformIntegrability import OAI.MathematicalPhysics.Boltzmann.Compactness.PrefixComparisonConvergence import OAI.MathematicalPhysics.Boltzmann.Branching.AveragedPairIntegrability import OAI.MathematicalPhysics.Boltzmann.Jets.SpatialCutoffIntegrability import OAI.MathematicalPhysics.Boltzmann.Branching.TightApproximation import OAI.MathematicalPhysics.Boltzmann.Compactness.NormalizedKernelAction import OAI.MathematicalPhysics.Boltzmann.Jets.FreeCoreGainKernel import OAI.MathematicalPhysics.Boltzmann.Collision.AxialSecondMismatch import OAI.MathematicalPhysics.Boltzmann.Jets.JetCoreConvergence import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricMesh import OAI.MathematicalPhysics.Boltzmann.Jets.JetCoreMomentBound import OAI.MathematicalPhysics.Boltzmann.Branching.HalfGaussianMoment import OAI.MathematicalPhysics.Boltzmann.Branching.BackgroundCappedLoss import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricPositiveCompact import OAI.MathematicalPhysics.Boltzmann.Branching.MediumStateCollision import OAI.MathematicalPhysics.Boltzmann.Branching.TimeSliceIntegration import OAI.MathematicalPhysics.Boltzmann.Collision.VelocityPolynomialBounds import OAI.MathematicalPhysics.Boltzmann.Collision.CollisionWeakMarginals import OAI.MathematicalPhysics.Boltzmann.Approximation.CutoffLossFrequency import OAI.MathematicalPhysics.Boltzmann.Jets.AnnularCollisionIntegrability import OAI.MathematicalPhysics.Boltzmann.Branching.DensityCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.OuterTightness import OAI.MathematicalPhysics.Boltzmann.Branching.RawPairCompactness import OAI.MathematicalPhysics.Boltzmann.Compactness.PairRepresentative import OAI.MathematicalPhysics.Boltzmann.Branching.IncomingLossRate import OAI.MathematicalPhysics.Boltzmann.Branching.NormalGainMeasureActions import OAI.MathematicalPhysics.Boltzmann.Branching.RadialReflectionChangeVariables import OAI.MathematicalPhysics.Boltzmann.Collision.SphereDirectionAbsolute import OAI.MathematicalPhysics.Boltzmann.Collision.GaussianWeightedConvergence import OAI.MathematicalPhysics.Boltzmann.Branching.ExponentialPairIntegrability import OAI.MathematicalPhysics.Boltzmann.Branching.MomentAverageBound import OAI.MathematicalPhysics.Boltzmann.Branching.AveragingTailSources import OAI.MathematicalPhysics.Boltzmann.Branching.ComplexWeakL2Diagonal import OAI.MathematicalPhysics.Boltzmann.Branching.MovingCutoffWeakLimit import OAI.MathematicalPhysics.Boltzmann.Collision.CollisionDissipation import OAI.MathematicalPhysics.Boltzmann.Approximation.CapLossScaling import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveSourceFormula import OAI.MathematicalPhysics.Boltzmann.Branching.NormalOutgoingSymmetry import OAI.MathematicalPhysics.Boltzmann.Collision.KernelInvariantPowers import OAI.MathematicalPhysics.Boltzmann.Branching.AeKernelHistoryOrder import OAI.MathematicalPhysics.Boltzmann.Collision.KernelInvariantOrder import OAI.MathematicalPhysics.Boltzmann.Compactness.FiniteDepthKernelOrder import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedVelocityIntegral import OAI.MathematicalPhysics.Boltzmann.Compactness.EntropyUniformIntegrability import OAI.MathematicalPhysics.Boltzmann.Collision.VelocityCutoffEntropyError import OAI.MathematicalPhysics.Boltzmann.Jets.TorusTransport import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalMomentIntegrability import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveAccessAngles import OAI.MathematicalPhysics.Boltzmann.Branching.AccessAngleStability import OAI.MathematicalPhysics.Boltzmann.Compactness.RenormalizedIntegrability import OAI.MathematicalPhysics.Boltzmann.Branching.GainEntropyTail import OAI.MathematicalPhysics.Boltzmann.Compactness.UniformIntegrableGainTail import OAI.MathematicalPhysics.Boltzmann.Compactness.L1TruncationCauchy import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedL1Tests import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakLinearMomentLimit import OAI.MathematicalPhysics.Boltzmann.Compactness.NormalizedCollisionRates import OAI.MathematicalPhysics.Boltzmann.Branching.SmoothedPrePostIdentity import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedPairUniformIntegrability import OAI.MathematicalPhysics.Boltzmann.Compactness.StrongPairMoment import OAI.MathematicalPhysics.Boltzmann.Compactness.PairPatchIdentity import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedTranslationTests import OAI.MathematicalPhysics.Boltzmann.Compactness.PairTranslatedProduct import OAI.MathematicalPhysics.Boltzmann.Branching.DoubleCollisionTests import OAI.MathematicalPhysics.Boltzmann.Collision.AngularGainTranslationTests import OAI.MathematicalPhysics.Boltzmann.Compactness.PairBoundedTruncation import OAI.MathematicalPhysics.Boltzmann.Branching.RelativeCutoffConvergence import OAI.MathematicalPhysics.Boltzmann.Collision.VelocitySmoothingError import OAI.MathematicalPhysics.Boltzmann.Compactness.L1VelocityTranslationApproximation import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedPairRate import OAI.MathematicalPhysics.Boltzmann.Compactness.PairPatchCover import OAI.MathematicalPhysics.Boltzmann.Branching.MixedPhysicalMeasures import OAI.MathematicalPhysics.Boltzmann.Collision.CollisionSources import OAI.MathematicalPhysics.Boltzmann.Branching.VanishingCutoffCollision import OAI.MathematicalPhysics.Boltzmann.Compactness.NormalizedPairCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedNormalizedGainTranslation import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalizedGainSmoothingAE import OAI.MathematicalPhysics.Boltzmann.Compactness.UniformGainTranslation import OAI.MathematicalPhysics.Boltzmann.Branching.GainSmoothingError import OAI.MathematicalPhysics.Boltzmann.Approximation.CutoffLipschitz import OAI.MathematicalPhysics.Boltzmann.Approximation.RegularizedCollisionDifference import OAI.MathematicalPhysics.Boltzmann.Compactness.EntropyDissipationAverage import OAI.MathematicalPhysics.Boltzmann.Compactness.KineticEntropyErrorLimit import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedEntropyProduction import OAI.MathematicalPhysics.Boltzmann.Approximation.RegularizedEntropyIntegrability import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalEntropyProduction import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedCollisionBlocks import OAI.MathematicalPhysics.Boltzmann.Compactness.EntropyRegularizationLimit import OAI.MathematicalPhysics.Boltzmann.Branching.ProductionDualLimit import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakL1ToWeakStar import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveIntegralFixedPoint import OAI.MathematicalPhysics.Boltzmann.Branching.DampedCollisionHistories import OAI.MathematicalPhysics.Boltzmann.Branching.DampedBranchingBlocks import OAI.MathematicalPhysics.Boltzmann.Collision.VelocityAverageDifference import OAI.MathematicalPhysics.Boltzmann.Branching.VariableSurvival import OAI.MathematicalPhysics.Boltzmann.Compactness.StrongMassClip import OAI.MathematicalPhysics.Boltzmann.Branching.AccessAngularFubini import OAI.MathematicalPhysics.Boltzmann.Branching.LogRenormalization import OAI.MathematicalPhysics.Boltzmann.Branching.LinearCharacteristicBalance import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveComparisonBound import OAI.MathematicalPhysics.Boltzmann.Approximation.RegularizedDissipationBound import OAI.MathematicalPhysics.Boltzmann.Approximation.CutoffEntropyMeasure import OAI.MathematicalPhysics.Boltzmann.Collision.GaussianLocalExistence import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakTimeLocalization import OAI.MathematicalPhysics.Boltzmann.Branching.CumulativeIntervalBalance import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakTimeBalance import OAI.MathematicalPhysics.Boltzmann.Branching.TruncatedExponential import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakTimeSurvival import OAI.MathematicalPhysics.Boltzmann.Branching.FlightMeasure import OAI.MathematicalPhysics.Boltzmann.Jets.ColdGaussianFamily import OAI.MathematicalPhysics.Boltzmann.Branching.IntegralSurvival import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveIntegralTime import OAI.MathematicalPhysics.Boltzmann.Branching.ZeroProfileParameters import OAI.MathematicalPhysics.Boltzmann.Branching.PhaseDecompositionNorm import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveIntegralPasting import OAI.MathematicalPhysics.Boltzmann.Branching.HotPhysicalSource import OAI.MathematicalPhysics.Boltzmann.Collision.GaussianColdPhysical import OAI.MathematicalPhysics.Boltzmann.Jets.JetColdLimitComparison import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedJetSolutions import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedHotRegularity import OAI.MathematicalPhysics.Boltzmann.Jets.ColdHotSourceDecomposition import OAI.MathematicalPhysics.Boltzmann.Branching.HotCollisionDecomposition import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedNetLoss import OAI.MathematicalPhysics.Boltzmann.Approximation.ColoredSourceDifferenceAE import OAI.MathematicalPhysics.Boltzmann.Branching.HotCanonicalFamily import OAI.MathematicalPhysics.Boltzmann.Branching.SliceUniformLimit import OAI.MathematicalPhysics.Boltzmann.Branching.SpaceTimeEssSup import OAI.MathematicalPhysics.Boltzmann.Branching.ClampedMildAE import OAI.MathematicalPhysics.Boltzmann.Branching.ClippedColdFiniteLimit import OAI.MathematicalPhysics.Boltzmann.Jets.ColdMildRepresentative import OAI.MathematicalPhysics.Boltzmann.Approximation.MildInitialAE import OAI.MathematicalPhysics.Boltzmann.Branching.RebuiltHotInitial import OAI.MathematicalPhysics.Boltzmann.Branching.ClippedColdTime import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveIntegralWindow import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedJetStability import OAI.MathematicalPhysics.Boltzmann.Jets.ColdFamilyGlobalStabilityAE import OAI.MathematicalPhysics.Boltzmann.Branching.ClippedColdShift import OAI.MathematicalPhysics.Boltzmann.Jets.PeriodicJetFamilies import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedHotGain import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicSourceBound import OAI.MathematicalPhysics.Boltzmann.Branching.CenteredPeriodicBound import OAI.MathematicalPhysics.Boltzmann.Branching.HotSeedCoreLower import OAI.MathematicalPhysics.Boltzmann.Branching.FamilyHotBounds import OAI.MathematicalPhysics.Boltzmann.Branching.RebuiltHotRegularity import OAI.MathematicalPhysics.Boltzmann.Jets.JetFamilyBounds import OAI.MathematicalPhysics.Boltzmann.Approximation.CapDilationScales import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicMildApproximation import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicFiniteMild import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicInitialEntropyLimit import OAI.MathematicalPhysics.Boltzmann.Branching.AttenuationGap import OAI.MathematicalPhysics.Boltzmann.Branching.RebuiltHotCapBound import OAI.MathematicalPhysics.Boltzmann.Branching.ShiftedStripe import OAI.MathematicalPhysics.Boltzmann.Collision.TransverseStripeWeak import OAI.MathematicalPhysics.Boltzmann.Jets.ThermalStripeIdentity import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricColdSource import OAI.MathematicalPhysics.Boltzmann.Jets.SpatialDilationAE import OAI.MathematicalPhysics.Boltzmann.Branching.SpaceTimeDilationAE import OAI.MathematicalPhysics.Boltzmann.Approximation.MildCharacteristics import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveIntegralBound import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedCharacteristic import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalCharacteristic import OAI.MathematicalPhysics.Boltzmann.Branching.EuclideanKineticMap import OAI.MathematicalPhysics.Boltzmann.Approximation.ResolventAverageBound import OAI.MathematicalPhysics.Boltzmann.Branching.LinearHotLocalization import OAI.MathematicalPhysics.Boltzmann.Branching.CharacteristicCoordinates import OAI.MathematicalPhysics.Boltzmann.Jets.JetContinuation import OAI.MathematicalPhysics.Boltzmann.Approximation.CapMomentBound import OAI.MathematicalPhysics.Boltzmann.Jets.JetFiniteCap import OAI.MathematicalPhysics.Boltzmann.Approximation.CappedDensitySequence import OAI.MathematicalPhysics.Boltzmann.Approximation.CapDilationCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.HotWindowInput import OAI.MathematicalPhysics.Boltzmann.Approximation.CapLabelFreeLimit import OAI.MathematicalPhysics.Boltzmann.Branching.HotWindowGeometry import OAI.MathematicalPhysics.Boltzmann.Approximation.CapHotUndamped import OAI.MathematicalPhysics.Boltzmann.Compactness.FiniteHorizonRatio import OAI.MathematicalPhysics.Boltzmann.Approximation.CapFiniteBackgroundLimit import OAI.MathematicalPhysics.Boltzmann.Branching.BackgroundBeamCloseness import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricDampedRetention import OAI.MathematicalPhysics.Boltzmann.Approximation.CapHotSourceIntegrability import OAI.MathematicalPhysics.Boltzmann.Approximation.CapColdBounds import OAI.MathematicalPhysics.Boltzmann.Approximation.CapColdAverages import OAI.MathematicalPhysics.Boltzmann.Approximation.SubcapColdControl import OAI.MathematicalPhysics.Boltzmann.Jets.ColdCentralVanishing import OAI.MathematicalPhysics.Boltzmann.Branching.HotChartHomeomorph import OAI.MathematicalPhysics.Boltzmann.Branching.CharacteristicProductTest import OAI.MathematicalPhysics.Boltzmann.Branching.TimeSourceCumulative import OAI.MathematicalPhysics.Boltzmann.Branching.ProjectedTimeBalance import OAI.MathematicalPhysics.Boltzmann.Branching.PhaseSourceMeasure import OAI.MathematicalPhysics.Boltzmann.Branching.OccupationSliceIntegral import OAI.MathematicalPhysics.Boltzmann.Approximation.MildCurveContinuity import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedMildBalance import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicMomentEntropy import OAI.MathematicalPhysics.Boltzmann.Branching.SpacetimeRelativeEntropy import OAI.MathematicalPhysics.Boltzmann.Branching.IntegrablePathTrace import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedAverageProducts import OAI.MathematicalPhysics.Boltzmann.Branching.RationalUniformApproximation import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicRenormalizedCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.RelativeEntropyMarginal import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakEntropyMarginal import OAI.MathematicalPhysics.Boltzmann.Compactness.StrongCompactPairTests import OAI.MathematicalPhysics.Boltzmann.Compactness.NormalizedGainCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.InitialLinearComparison import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakConservedMarginal import OAI.MathematicalPhysics.Boltzmann.Branching.LinearSurvivalIdentity import OAI.MathematicalPhysics.Boltzmann.Approximation.SurvivalVolterraIntegrable import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveVolterra import OAI.MathematicalPhysics.Boltzmann.Branching.EuclideanBackwardMap import OAI.MathematicalPhysics.Boltzmann.Branching.HotPositiveRegion import OAI.MathematicalPhysics.Boltzmann.Branching.WeakCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.CharacteristicCutoffGeometry import OAI.MathematicalPhysics.Boltzmann.Branching.TransportedKernelRestriction import OAI.MathematicalPhysics.Boltzmann.Collision.KernelConjugacy import OAI.MathematicalPhysics.Boltzmann.Branching.SmallFirstGain import OAI.MathematicalPhysics.Boltzmann.Collision.SheetKernelLimits import OAI.MathematicalPhysics.Boltzmann.Branching.LateBoxAccessMeasure import OAI.MathematicalPhysics.Boltzmann.Jets.AnnularTightness import OAI.MathematicalPhysics.Boltzmann.Approximation.CappedTightness import OAI.MathematicalPhysics.Boltzmann.Branching.CompactCapFamily import OAI.MathematicalPhysics.Boltzmann.Jets.TorusCharacteristic import OAI.MathematicalPhysics.Boltzmann.Branching.CellLocalizedSource import OAI.MathematicalPhysics.Boltzmann.Branching.InteriorCell import OAI.MathematicalPhysics.Boltzmann.Branching.WindowLocalizedSource import OAI.MathematicalPhysics.Boltzmann.Branching.SupportedTransportTest import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalL1ApproximationLimit import OAI.MathematicalPhysics.Boltzmann.Approximation.CapHotTransportBalance import OAI.MathematicalPhysics.Boltzmann.Branching.HotPairWindowGeometry import OAI.MathematicalPhysics.Boltzmann.Branching.TightCapFamily import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakCapOuterBound import OAI.MathematicalPhysics.Boltzmann.Approximation.CapPairMoments import OAI.MathematicalPhysics.Boltzmann.Branching.ProductKineticCutoff import OAI.MathematicalPhysics.Boltzmann.Approximation.CapWeightedNonlinearLimit import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveNonlinearLimit import OAI.MathematicalPhysics.Boltzmann.Approximation.CapNonlinearHotLimit import OAI.MathematicalPhysics.Boltzmann.Compactness.KineticWindowL1 import OAI.MathematicalPhysics.Boltzmann.Compactness.UniformIntegrableCoordinates import OAI.MathematicalPhysics.Boltzmann.Collision.FourierCompactness import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalFrequencyWindow import OAI.MathematicalPhysics.Boltzmann.Branching.SpacetimeAverageLimit import OAI.MathematicalPhysics.Boltzmann.Collision.VelocityAverageRepresentatives import OAI.MathematicalPhysics.Boltzmann.Jets.TorusVelocityWindowAE import OAI.MathematicalPhysics.Boltzmann.Compactness.WeakDuhamelLimit import OAI.MathematicalPhysics.Boltzmann.Approximation.CapMildLimit import OAI.MathematicalPhysics.Boltzmann.Approximation.MildRenormalization import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveMildRepresentative import OAI.MathematicalPhysics.Boltzmann.Compactness.StrongMildRepresentative import OAI.MathematicalPhysics.Boltzmann.Compactness.L1CurveEquality import OAI.MathematicalPhysics.Boltzmann.Approximation.MildRenormalizedBalance import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalAdmissibility import OAI.MathematicalPhysics.Boltzmann.Branching.EnergyCollisionMarginals import OAI.MathematicalPhysics.Boltzmann.Collision.CollisionConservation import OAI.MathematicalPhysics.Boltzmann.Compactness.EntropyDissipationCoordinates import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalDissipationBridge import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedMildEntropyLimit import OAI.MathematicalPhysics.Boltzmann.Branching.MomentumCollisionIntegrability import OAI.MathematicalPhysics.Boltzmann.Approximation.MildConservation import OAI.MathematicalPhysics.Boltzmann.Compactness.RenormalizedCollisionIntegrability import OAI.MathematicalPhysics.Boltzmann.Branching.RateDissipationMonotone import OAI.MathematicalPhysics.Boltzmann.Approximation.MassNormalizedCollisionLimits import OAI.MathematicalPhysics.Boltzmann.Compactness.FiniteRatesWindowUI import OAI.MathematicalPhysics.Boltzmann.Branching.WindowCollisionMarginal import OAI.MathematicalPhysics.Boltzmann.Branching.ClippedProductionLimit import OAI.MathematicalPhysics.Boltzmann.Branching.DissipationMassExhaustion import OAI.MathematicalPhysics.Boltzmann.Branching.FullDissipationLimit import OAI.MathematicalPhysics.Boltzmann.Approximation.CapEntropyMoments import OAI.MathematicalPhysics.Boltzmann.Approximation.SubcapMildLimits import OAI.MathematicalPhysics.Boltzmann.Compactness.EntropyLocalConstruction import OAI.MathematicalPhysics.Boltzmann.Approximation.MildLocalAdmissibility import OAI.MathematicalPhysics.Boltzmann.Approximation.CapLocalAdmissibility import OAI.MathematicalPhysics.Boltzmann.Approximation.SubcapCapLocalAdmissibility import OAI.MathematicalPhysics.Boltzmann.Approximation.DormantConstruction import OAI.MathematicalPhysics.Boltzmann.Branching.SmallDilationGeometry import OAI.MathematicalPhysics.Boltzmann.Approximation.DormantBoxLimit import OAI.MathematicalPhysics.Boltzmann.Branching.SeparationBoxContainment import OAI.MathematicalPhysics.Boltzmann.Branching.OffAxisBoxExhaustion import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveVolterraOffAxisAE import OAI.MathematicalPhysics.Boltzmann.Jets.FreeCoreMismatch import OAI.MathematicalPhysics.Boltzmann.Collision.AxialBandMeasure import OAI.MathematicalPhysics.Boltzmann.Branching.SecondCoreOffBands import OAI.MathematicalPhysics.Boltzmann.Branching.DilatedCoreDensity import OAI.MathematicalPhysics.Boltzmann.Jets.FreeCoreSharpBound import OAI.MathematicalPhysics.Boltzmann.Branching.TranslatedCoreKernel import OAI.MathematicalPhysics.Boltzmann.Branching.MainCoreScaleWindow import OAI.MathematicalPhysics.Boltzmann.Compactness.SelectedCoreSelection import OAI.MathematicalPhysics.Boltzmann.Jets.CoreDensityTranslation import OAI.MathematicalPhysics.Boltzmann.Branching.TwoCoreLimit import OAI.MathematicalPhysics.Boltzmann.Branching.DilatedTwoCoreLimit import OAI.MathematicalPhysics.Boltzmann.Jets.ThermalPointBounds import OAI.MathematicalPhysics.Boltzmann.Branching.RedundantParameterSupport import OAI.MathematicalPhysics.Boltzmann.Jets.CoreParameterStep import OAI.MathematicalPhysics.Boltzmann.Branching.RescaledParameterSlab import OAI.MathematicalPhysics.Boltzmann.Jets.CoreJointParameterDensity import OAI.MathematicalPhysics.Boltzmann.Collision.CarlemanIdentity import OAI.MathematicalPhysics.Boltzmann.Branching.NearbyMainCopies import OAI.MathematicalPhysics.Boltzmann.Branching.MainPositiveRemainderBound import OAI.MathematicalPhysics.Boltzmann.Compactness.KineticDilationIntegral import OAI.MathematicalPhysics.Boltzmann.Branching.DilationBoxOrder import OAI.MathematicalPhysics.Boltzmann.Approximation.CapActualLossDensity import OAI.MathematicalPhysics.Boltzmann.Approximation.SurvivalProfile import OAI.MathematicalPhysics.Boltzmann.Branching.UnitNormalizedResidual import OAI.MathematicalPhysics.Boltzmann.Branching.LossResidualLimit import OAI.MathematicalPhysics.Boltzmann.Branching.MaxwellianFrequency import OAI.MathematicalPhysics.Boltzmann.Compactness.ContinuationAdmissibility import OAI.MathematicalPhysics.Boltzmann.Branching.BackwardCellBound import OAI.MathematicalPhysics.Boltzmann.Branching.MovingBoxMass import OAI.MathematicalPhysics.Boltzmann.Branching.UpperTimeDeletion import OAI.MathematicalPhysics.Boltzmann.Branching.FiveGainPullback import OAI.MathematicalPhysics.Boltzmann.Branching.StageParameterIntegration import OAI.MathematicalPhysics.Boltzmann.Compactness.FiniteParameterChain import OAI.MathematicalPhysics.Boltzmann.Jets.ThermalParameterChain import OAI.MathematicalPhysics.Boltzmann.Branching.ControlledParameterPath import OAI.MathematicalPhysics.Boltzmann.Branching.WeightedThermalChain import OAI.MathematicalPhysics.Boltzmann.Branching.FiveGainConvergence import OAI.MathematicalPhysics.Boltzmann.Compactness.FiniteThermalLimit import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricTwoCoreUniform import OAI.MathematicalPhysics.Boltzmann.Branching.TranslatedTwoCoreLimit import OAI.MathematicalPhysics.Boltzmann.Compactness.SelectedLargeOutput import OAI.MathematicalPhysics.Boltzmann.Jets.OriginMeshStep import OAI.MathematicalPhysics.Boltzmann.Branching.RetainedAxialDecay import OAI.MathematicalPhysics.Boltzmann.Collision.AxialDecayLimit import OAI.MathematicalPhysics.Boltzmann.Compactness.SelectedTwoGainLimit import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveRestrictedChain import OAI.MathematicalPhysics.Boltzmann.Branching.RestrictedCone import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedMeshStep import OAI.MathematicalPhysics.Boltzmann.Branching.FirstEntryMass import OAI.MathematicalPhysics.Boltzmann.Jets.OriginMeshLimit import OAI.MathematicalPhysics.Boltzmann.Branching.CentralRetainedLimit import OAI.MathematicalPhysics.Boltzmann.Branching.AverageFourierTail import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedAverageCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.CommonBoundedAverageCompactness import OAI.MathematicalPhysics.Boltzmann.Compactness.UniformAverageCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.VelocityAveraging import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicWeakCompactness import OAI.MathematicalPhysics.Boltzmann.Branching.EnergyTruncation import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicJointBudgetLimit import OAI.MathematicalPhysics.Boltzmann.Compactness.EntropyCollisionIntegrability import OAI.MathematicalPhysics.Boltzmann.Branching.ClippedCharacteristicGain import OAI.MathematicalPhysics.Boltzmann.Branching.CharacteristicPhysicalGain import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicStrongAverages import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveContributionsIntegrable import OAI.MathematicalPhysics.Boltzmann.Collision.ScalarEntropyJointTrace import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalizedGainCompactness import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicFiniteGainStrong import OAI.MathematicalPhysics.Boltzmann.Branching.GainMeasureLimit import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicCharacteristicGainUnit import OAI.MathematicalPhysics.Boltzmann.Collision.CollisionComparisonError import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicDensityStrong import OAI.MathematicalPhysics.Boltzmann.Branching.LimitFullPositiveSurvival import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalLinearContinuous import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicLinearApproximation import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalEvolution import OAI.MathematicalPhysics.Boltzmann.Branching.MarkedWaitLower import OAI.MathematicalPhysics.Boltzmann.Branching.DampedEndpointHistories import OAI.MathematicalPhysics.Boltzmann.Compactness.SelectedOriginDeletion import OAI.MathematicalPhysics.Boltzmann.Branching.ThreeCollisionTimes import OAI.MathematicalPhysics.Boltzmann.Collision.CollisionParameterShuffle import OAI.MathematicalPhysics.Boltzmann.Branching.ThreeSelectedIntegral import OAI.MathematicalPhysics.Boltzmann.Branching.EntrySites import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricEntry import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalGlobalRenormalized import OAI.MathematicalPhysics.Boltzmann.Branching.MediumEndpointTransport import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalGainTransport import OAI.MathematicalPhysics.Boltzmann.Jets.BeamNormalOutgoing import OAI.MathematicalPhysics.Boltzmann.Branching.ScaledBoundedEvent import OAI.MathematicalPhysics.Boltzmann.Branching.DampedLocalBeamBlock import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalBeamBlock import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricAnnularFrequency import OAI.MathematicalPhysics.Boltzmann.Branching.DampedBoundedEndpointTransport import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedGeometricBlock import OAI.MathematicalPhysics.Boltzmann.Branching.ScaledBlockMass import OAI.MathematicalPhysics.Boltzmann.Collision.CollisionWaitingCone import OAI.MathematicalPhysics.Boltzmann.Jets.BeamNormalCharacteristicIdentity import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalizedDampedBalance import OAI.MathematicalPhysics.Boltzmann.Branching.DampedLateBoxPhysicalBlock import OAI.MathematicalPhysics.Boltzmann.Branching.LateBoxCommonDamping import OAI.MathematicalPhysics.Boltzmann.Jets.BeamGainNormalOrder import OAI.MathematicalPhysics.Boltzmann.Branching.FlightConeLocalization import OAI.MathematicalPhysics.Boltzmann.Branching.SeedEscapeMeasure import OAI.MathematicalPhysics.Boltzmann.Compactness.FiniteEntryPhaseBound import OAI.MathematicalPhysics.Boltzmann.Compactness.SelectedWindowDeletion import OAI.MathematicalPhysics.Boltzmann.Branching.RetainedWindowDeletion import OAI.MathematicalPhysics.Boltzmann.Compactness.SelectedNonaxialLimit import OAI.MathematicalPhysics.Boltzmann.Branching.RescaledColdMajorant import OAI.MathematicalPhysics.Boltzmann.Compactness.SelectedRemainderMeasure import OAI.MathematicalPhysics.Boltzmann.Branching.RescaledBoundedGain import OAI.MathematicalPhysics.Boltzmann.Branching.PhaseSliceLocalization import OAI.MathematicalPhysics.Boltzmann.Branching.BoundedEntryPortion import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalizedBlockComparison import OAI.MathematicalPhysics.Boltzmann.Compactness.PhysicalGainStrictTime import OAI.MathematicalPhysics.Boltzmann.Compactness.FiniteGainHistoryComparison import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricLocalizedEntry import OAI.MathematicalPhysics.Boltzmann.Branching.CommonHistoryCore import OAI.MathematicalPhysics.Boltzmann.Branching.EndpointHistoryMass import OAI.MathematicalPhysics.Boltzmann.Approximation.PositiveEndpointHistory import OAI.MathematicalPhysics.Boltzmann.Compactness.LocalizedHotMassGrowth import OAI.MathematicalPhysics.Boltzmann.Branching.AeLocalizedHotMassGrowth import OAI.MathematicalPhysics.Boltzmann.Jets.GeometricCommonBlock import OAI.MathematicalPhysics.Boltzmann.Branching.CommonStartGeometry import OAI.MathematicalPhysics.Boltzmann.Jets.AnnularCharacteristicCutoff import OAI.MathematicalPhysics.Boltzmann.Compactness.PeriodicExistenceDischarge import OAI.MathematicalPhysics.Boltzmann.Approximation.CapMixedCollisionLimits import OAI.MathematicalPhysics.Boltzmann.Approximation.CapLimitTransport import OAI.MathematicalPhysics.Boltzmann.Approximation.CapMixedPositiveBound import OAI.MathematicalPhysics.Boltzmann.Branching.HotRatioCollisionTrace import OAI.MathematicalPhysics.Boltzmann.Approximation.CapCoefficientExtraction import OAI.MathematicalPhysics.Boltzmann.Approximation.MildDensityAgreement import OAI.MathematicalPhysics.Boltzmann.Branching.ScaledMassAgreement import OAI.MathematicalPhysics.Boltzmann.Branching.DiagonalVanishingCap import OAI.MathematicalPhysics.Boltzmann.Approximation.CapCoveredDamping import OAI.MathematicalPhysics.Boltzmann.Compactness.KineticEndpointCoordinates import OAI.MathematicalPhysics.Boltzmann.Approximation.CapEscapingSeed import OAI.MathematicalPhysics.Boltzmann.Branching.HotFullVanishingContradiction import OAI.MathematicalPhysics.Boltzmann.Approximation.CapAnnularMassGrowth import OAI.MathematicalPhysics.Boltzmann.Approximation.CapUniformFiniteHorizon import OAI.MathematicalPhysics.Boltzmann.Branching.MainParameters import OAI.MathematicalPhysics.Boltzmann.Branching.ConditionalMain import OAI.MathematicalPhysics.Boltzmann.Branching.PeriodicExistenceReduction import OAI.MathematicalPhysics.Boltzmann.UnconditionalMainProof import OAI.MathematicalPhysics.Boltzmann.Main import OAI.MathematicalPhysics.Boltzmann.Jets.JetZeroControl