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

Definition

KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_LinearImage

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.LinearImage 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.Basic, FunctionalInequalities.KLS.LogConcave.Isotropic, FunctionalInequalities.Probability.LogConcave, FunctionalInequalities.KLS.LogConcave.Density.AbsoluteContinuity, FunctionalInequalities.KLS.LogConcave.Density.BorellRepresentation.Basic, FunctionalInequalities.KLS.LogConcave.Density.BorellRepresentation.Construction, FunctionalInequalities.Probability.AffineSupport, and FunctionalInequalities.Probability.Transport.

Original module imports

import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic
import FunctionalInequalities.KLS.LogConcave.Isotropic
import FunctionalInequalities.Probability.LogConcave
import FunctionalInequalities.KLS.LogConcave.Density.AbsoluteContinuity
import FunctionalInequalities.KLS.LogConcave.Density.BorellRepresentation.Basic
import FunctionalInequalities.KLS.LogConcave.Density.BorellRepresentation.Construction
import FunctionalInequalities.Probability.AffineSupport
import FunctionalInequalities.Probability.Transport

Module navigation

Direct project imports: KLS/LogConcave/Density/GaussianSmoothing/Basic, KLS/LogConcave/Isotropic, Probability/LogConcave, KLS/LogConcave/Density/AbsoluteContinuity, KLS/LogConcave/Density/BorellRepresentation/Basic, KLS/LogConcave/Density/BorellRepresentation/Construction, Probability/AffineSupport, Probability/Transport.

Theorems in source order:

gaussian_product_latent_map

Project result: The KLS conjecture.

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

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Isotropic
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_LogConcave
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_AbsoluteContinuity
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_BorellRepresentation_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_BorellRepresentation_Construction
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_AffineSupport
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/LinearImage.lean#L1-L71 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.LinearImage`, import-context bundle `KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_LinearImage`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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