Import context: KLS/Letwin/RegularClass

Definition

KLSModular_FunctionalInequalities_KLS_Letwin_RegularClass

by Lazyfill · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

functional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-context

This bundle retains the import context of the source module FunctionalInequalities.KLS.Letwin.RegularClass in the modular KLS dependency graph. It adds no new mathematical declarations. Substantive statements and proofs are represented by separate theorem nodes.

Its direct project prerequisite modules are FunctionalInequalities.Analysis.Operator.HilbertSchmidt, FunctionalInequalities.KLS.CEK.MomentRegularity.TraceStein, FunctionalInequalities.KLS.IsotropicSupport, FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.QuadraticVariance, FunctionalInequalities.Probability.Stein.QuadraticAction, FunctionalInequalities.Analysis.BakryEmery.Calculus, FunctionalInequalities.Analysis.BakryEmery.Cumulant.Basic, FunctionalInequalities.Analysis.Matrix.Sign, FunctionalInequalities.Analysis.Operator.Coordinates, FunctionalInequalities.Probability.Stein.Kernel, FunctionalInequalities.Analysis.BakryEmery.HessianOperator, FunctionalInequalities.Analysis.BakryEmery.WeakHessian, FunctionalInequalities.Analysis.WeakDerivative.Basic, FunctionalInequalities.Probability.LogConcave, FunctionalInequalities.KLS.Isotropic, FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic, FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments, FunctionalInequalities.KLS.LogConcave.Density.Tilted, FunctionalInequalities.Probability.AffineSupport, FunctionalInequalities.Probability.QuadraticVariance, and FunctionalInequalities.Probability.Transport.

Original module imports

import FunctionalInequalities.Analysis.Operator.HilbertSchmidt
import FunctionalInequalities.KLS.CEK.MomentRegularity.TraceStein
import FunctionalInequalities.KLS.IsotropicSupport
import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.QuadraticVariance
import FunctionalInequalities.Probability.Stein.QuadraticAction
import FunctionalInequalities.Analysis.BakryEmery.Calculus
import FunctionalInequalities.Analysis.BakryEmery.Cumulant.Basic
import FunctionalInequalities.Analysis.Matrix.Sign
import FunctionalInequalities.Analysis.Operator.Coordinates
import FunctionalInequalities.Probability.Stein.Kernel
import FunctionalInequalities.Analysis.BakryEmery.HessianOperator
import FunctionalInequalities.Analysis.BakryEmery.WeakHessian
import FunctionalInequalities.Analysis.WeakDerivative.Basic
import FunctionalInequalities.Probability.LogConcave
import FunctionalInequalities.KLS.Isotropic
import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic
import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments
import FunctionalInequalities.KLS.LogConcave.Density.Tilted
import FunctionalInequalities.Probability.AffineSupport
import FunctionalInequalities.Probability.QuadraticVariance
import FunctionalInequalities.Probability.Transport

Module navigation

Direct project imports: Analysis/Operator/HilbertSchmidt, KLS/CEK/MomentRegularity/TraceStein, KLS/IsotropicSupport, KLS/LogConcave/Density/GaussianSmoothing/QuadraticVariance, Probability/Stein/QuadraticAction, Analysis/BakryEmery/Calculus, Analysis/BakryEmery/Cumulant/Basic, Analysis/Matrix/Sign, Analysis/Operator/Coordinates, Probability/Stein/Kernel, Analysis/BakryEmery/HessianOperator, Analysis/BakryEmery/WeakHessian, Analysis/WeakDerivative/Basic, Probability/LogConcave, KLS/Isotropic, KLS/LogConcave/Density/GaussianSmoothing/Basic, KLS/LogConcave/Density/GaussianSmoothing/Moments, KLS/LogConcave/Density/Tilted, Probability/AffineSupport, Probability/QuadraticVariance, Probability/Transport.

Theorems in source order:

regularClass_matrix_variance_le_eight

Project result: The KLS conjecture.

Original module · FunctionalInequalities.KLS.Letwin.RegularClass · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Operator_HilbertSchmidt
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_TraceStein
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_IsotropicSupport
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_QuadraticVariance
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Stein_QuadraticAction
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Calculus
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Cumulant_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_Sign
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Operator_Coordinates
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Stein_Kernel
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_HessianOperator
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_WeakHessian
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_WeakDerivative_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_LogConcave
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_Isotropic
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Moments
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_Tilted
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_AffineSupport
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_QuadraticVariance
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Transport

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/KLS/Letwin/RegularClass.lean#L1-L219 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.Letwin.RegularClass`, import-context bundle `KLSModular_FunctionalInequalities_KLS_Letwin_RegularClass`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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