Import context: KLS/LogConcave/Density/GaussianSmoothing/ProductCoupling

Definition

KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_ProductCoupling

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.LogConcave.Density.GaussianSmoothing.ProductCoupling 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.KLS.LogConcave.Density.GaussianSmoothing.LinearImage, FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments, FunctionalInequalities.KLS.LogConcave.HessianStein, FunctionalInequalities.Analysis.BakryEmery.Calculus, FunctionalInequalities.Energy.WeightedGradient.Core, FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic, FunctionalInequalities.L2.Pairing, FunctionalInequalities.Probability.Stein.Kernel, FunctionalInequalities.Probability.Stein.SourceDualBound, FunctionalInequalities.Analysis.BakryEmery.HessianOperator, FunctionalInequalities.Analysis.BakryEmery.WeakHessian, and FunctionalInequalities.Probability.Stein.HessianKernel. It also directly imports the external prerequisite modules Mathlib.MeasureTheory.Measure.RegularityCompacts and Mathlib.Topology.UniformSpace.Uniformizable.

Original module imports

import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.LinearImage
import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments
import FunctionalInequalities.KLS.LogConcave.HessianStein
import Mathlib.MeasureTheory.Measure.RegularityCompacts
import Mathlib.Topology.UniformSpace.Uniformizable
import FunctionalInequalities.Analysis.BakryEmery.Calculus
import FunctionalInequalities.Energy.WeightedGradient.Core
import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic
import FunctionalInequalities.L2.Pairing
import FunctionalInequalities.Probability.Stein.Kernel
import FunctionalInequalities.Probability.Stein.SourceDualBound
import FunctionalInequalities.Analysis.BakryEmery.HessianOperator
import FunctionalInequalities.Analysis.BakryEmery.WeakHessian
import FunctionalInequalities.Probability.Stein.HessianKernel

Module navigation

Direct project imports: KLS/LogConcave/Density/GaussianSmoothing/LinearImage, KLS/LogConcave/Density/GaussianSmoothing/Moments, KLS/LogConcave/HessianStein, Analysis/BakryEmery/Calculus, Energy/WeightedGradient/Core, KLS/LogConcave/Density/GaussianSmoothing/Basic, L2/Pairing, Probability/Stein/Kernel, Probability/Stein/SourceDualBound, Analysis/BakryEmery/HessianOperator, Analysis/BakryEmery/WeakHessian, Probability/Stein/HessianKernel.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.ProductCoupling · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_LinearImage
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Moments
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_HessianStein
import Mathlib.MeasureTheory.Measure.RegularityCompacts
import Mathlib.Topology.UniformSpace.Uniformizable
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Calculus
import Definitions.Def_KLSModular_FunctionalInequalities_Energy_WeightedGradient_Core
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_L2_Pairing
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Stein_Kernel
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Stein_SourceDualBound
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_HessianOperator
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_WeakHessian
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Stein_HessianKernel

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/KLS/LogConcave/Density/GaussianSmoothing/ProductCoupling.lean#L1-L280 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.ProductCoupling`, import-context bundle `KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_ProductCoupling`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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