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

Definition

KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_QuadraticVariance

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.QuadraticVariance 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.ProductCoupling, FunctionalInequalities.KLS.LogConcave.HminusOne, FunctionalInequalities.Probability.QuadraticVariance, FunctionalInequalities.Analysis.BakryEmery.Calculus, FunctionalInequalities.Probability.LogConcave, FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic, FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.LinearImage, FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments, FunctionalInequalities.Probability.AffineSupport, FunctionalInequalities.Probability.Moments, FunctionalInequalities.Probability.Stein.Kernel, FunctionalInequalities.Analysis.BakryEmery.HessianOperator, and FunctionalInequalities.Probability.Transport.

Original module imports

import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.ProductCoupling
import FunctionalInequalities.KLS.LogConcave.HminusOne
import FunctionalInequalities.Probability.QuadraticVariance
import FunctionalInequalities.Analysis.BakryEmery.Calculus
import FunctionalInequalities.Probability.LogConcave
import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic
import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.LinearImage
import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments
import FunctionalInequalities.Probability.AffineSupport
import FunctionalInequalities.Probability.Moments
import FunctionalInequalities.Probability.Stein.Kernel
import FunctionalInequalities.Analysis.BakryEmery.HessianOperator
import FunctionalInequalities.Probability.Transport

Module navigation

Direct project imports: KLS/LogConcave/Density/GaussianSmoothing/ProductCoupling, KLS/LogConcave/HminusOne, Probability/QuadraticVariance, Analysis/BakryEmery/Calculus, Probability/LogConcave, KLS/LogConcave/Density/GaussianSmoothing/Basic, KLS/LogConcave/Density/GaussianSmoothing/LinearImage, KLS/LogConcave/Density/GaussianSmoothing/Moments, Probability/AffineSupport, Probability/Moments, Probability/Stein/Kernel, Analysis/BakryEmery/HessianOperator, Probability/Transport.

Theorems in source order:

gaussian_smoothed_quadratic_variance_le_latent_energy

Project result: The KLS conjecture.

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

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_ProductCoupling
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_HminusOne
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_QuadraticVariance
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Calculus
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_LogConcave
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Basic
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_Probability_AffineSupport
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Moments
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Stein_Kernel
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_HessianOperator
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Transport

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/KLS/LogConcave/Density/GaussianSmoothing/QuadraticVariance.lean#L1-L160 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.QuadraticVariance`, import-context bundle `KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_QuadraticVariance`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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