Import context: KLS/CEK/MomentRegularity/TraceStein

Definition

KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_TraceStein

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.CEK.MomentRegularity.TraceStein 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.BakryEmery.Bochner.Basic, FunctionalInequalities.Analysis.BakryEmery.HessianOperator, FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.InverseHessian.Basic, FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.LipschitzHessian, FunctionalInequalities.Analysis.BakryEmery.MongeAmpere, FunctionalInequalities.Analysis.BakryEmery.WeakHessian, FunctionalInequalities.Analysis.Cutoff.Conservativity, FunctionalInequalities.Analysis.Matrix.Integral, FunctionalInequalities.Analysis.Matrix.Positivity, FunctionalInequalities.Analysis.Matrix.TraceGram, FunctionalInequalities.Analysis.Matrix.WeakDerivative, FunctionalInequalities.Analysis.Matrix.WeakTrace, FunctionalInequalities.Analysis.WeakDerivative.Basic, FunctionalInequalities.KLS.Isotropic, FunctionalInequalities.KLS.LogConcave.HessianStein, FunctionalInequalities.KLS.LogConcave.HessianTrace, and FunctionalInequalities.KLS.CEK.MomentRegularity.Cutoff.

Original module imports

import FunctionalInequalities.Analysis.BakryEmery.Bochner.Basic
import FunctionalInequalities.Analysis.BakryEmery.HessianOperator
import FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.InverseHessian.Basic
import FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.LipschitzHessian
import FunctionalInequalities.Analysis.BakryEmery.MongeAmpere
import FunctionalInequalities.Analysis.BakryEmery.WeakHessian
import FunctionalInequalities.Analysis.Cutoff.Conservativity
import FunctionalInequalities.Analysis.Matrix.Integral
import FunctionalInequalities.Analysis.Matrix.Positivity
import FunctionalInequalities.Analysis.Matrix.TraceGram
import FunctionalInequalities.Analysis.Matrix.WeakDerivative
import FunctionalInequalities.Analysis.Matrix.WeakTrace
import FunctionalInequalities.Analysis.WeakDerivative.Basic
import FunctionalInequalities.KLS.Isotropic
import FunctionalInequalities.KLS.LogConcave.HessianStein
import FunctionalInequalities.KLS.LogConcave.HessianTrace
import FunctionalInequalities.KLS.CEK.MomentRegularity.Cutoff

Module navigation

Direct project imports: Analysis/BakryEmery/Bochner/Basic, Analysis/BakryEmery/HessianOperator, Analysis/BakryEmery/IntegrationByParts/InverseHessian/Basic, Analysis/BakryEmery/IntegrationByParts/LipschitzHessian, Analysis/BakryEmery/MongeAmpere, Analysis/BakryEmery/WeakHessian, Analysis/Cutoff/Conservativity, Analysis/Matrix/Integral, Analysis/Matrix/Positivity, Analysis/Matrix/TraceGram, Analysis/Matrix/WeakDerivative, Analysis/Matrix/WeakTrace, Analysis/WeakDerivative/Basic, KLS/Isotropic, KLS/LogConcave/HessianStein, KLS/LogConcave/HessianTrace, KLS/CEK/MomentRegularity/Cutoff.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.KLS.CEK.MomentRegularity.TraceStein · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Bochner_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_HessianOperator
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_InverseHessian_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_LipschitzHessian
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_MongeAmpere
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_WeakHessian
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Cutoff_Conservativity
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_Integral
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_Positivity
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_TraceGram
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_WeakDerivative
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_WeakTrace
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_WeakDerivative_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_Isotropic
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_HessianStein
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_HessianTrace
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_Cutoff

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/KLS/CEK/MomentRegularity/TraceStein.lean#L1-L2486 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.CEK.MomentRegularity.TraceStein`, import-context bundle `KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_TraceStein`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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