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Import context: KLS/LogConcave/WeightedGradient/Kernel

Definition
KLSModular_FunctionalInequalities_KLS_LogConcave_WeightedGradient_Kernel

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.WeightedGradient.Kernel 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.WeightedGradient.Multiplier, FunctionalInequalities.Energy.Euclidean.WeakDerivative, FunctionalInequalities.L2.MeanVariance, FunctionalInequalities.KLS.LogConcave.Density.Tilted, and FunctionalInequalities.Energy.Euclidean.ZeroGradient. It also directly imports the external prerequisite module Mathlib.MeasureTheory.Measure.Tilted.

Original module imports

import FunctionalInequalities.KLS.LogConcave.WeightedGradient.Multiplier
import FunctionalInequalities.Energy.Euclidean.WeakDerivative
import FunctionalInequalities.L2.MeanVariance
import FunctionalInequalities.KLS.LogConcave.Density.Tilted
import FunctionalInequalities.Energy.Euclidean.ZeroGradient
import Mathlib.MeasureTheory.Measure.Tilted

Module navigation

Direct project imports: KLS/LogConcave/WeightedGradient/Multiplier, Energy/Euclidean/WeakDerivative, L2/MeanVariance, KLS/LogConcave/Density/Tilted, Energy/Euclidean/ZeroGradient.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.KLS.LogConcave.WeightedGradient.Kernel · Frozen source 408915f.

Definition code
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_WeightedGradient_Multiplier
import Definitions.Def_KLSModular_FunctionalInequalities_Energy_Euclidean_WeakDerivative
import Definitions.Def_KLSModular_FunctionalInequalities_L2_MeanVariance
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_Tilted
import Definitions.Def_KLSModular_FunctionalInequalities_Energy_Euclidean_ZeroGradient
import Mathlib.MeasureTheory.Measure.Tilted
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/KLS/LogConcave/WeightedGradient/Kernel.lean#L1-L472 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.LogConcave.WeightedGradient.Kernel`, import-context bundle `KLSModular_FunctionalInequalities_KLS_LogConcave_WeightedGradient_Kernel`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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