Import context: KLS/CEK/MomentRegularity/Potential

Definition

KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_Potential

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.Potential 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.HessianOperator, FunctionalInequalities.Analysis.BakryEmery.WeakHessian, FunctionalInequalities.Analysis.Convex.Alexandrov, FunctionalInequalities.Analysis.Convex.Caffarelli, FunctionalInequalities.Analysis.Convex.GradientLipschitz, FunctionalInequalities.Analysis.Convex.HessianRegularity, FunctionalInequalities.Analysis.Convex.Subgradient, FunctionalInequalities.Analysis.Convex.Viscosity, FunctionalInequalities.KLS.CEK.MomentMap, FunctionalInequalities.KLS.Isotropic, and FunctionalInequalities.Probability.Stein.HessianKernel.

Original module imports

import FunctionalInequalities.Analysis.BakryEmery.HessianOperator
import FunctionalInequalities.Analysis.BakryEmery.WeakHessian
import FunctionalInequalities.Analysis.Convex.Alexandrov
import FunctionalInequalities.Analysis.Convex.Caffarelli
import FunctionalInequalities.Analysis.Convex.GradientLipschitz
import FunctionalInequalities.Analysis.Convex.HessianRegularity
import FunctionalInequalities.Analysis.Convex.Subgradient
import FunctionalInequalities.Analysis.Convex.Viscosity
import FunctionalInequalities.KLS.CEK.MomentMap
import FunctionalInequalities.KLS.Isotropic
import FunctionalInequalities.Probability.Stein.HessianKernel

Module navigation

Direct project imports: Analysis/BakryEmery/HessianOperator, Analysis/BakryEmery/WeakHessian, Analysis/Convex/Alexandrov, Analysis/Convex/Caffarelli, Analysis/Convex/GradientLipschitz, Analysis/Convex/HessianRegularity, Analysis/Convex/Subgradient, Analysis/Convex/Viscosity, KLS/CEK/MomentMap, KLS/Isotropic, Probability/Stein/HessianKernel.

Theorems in source order:

exists_regular_moment_potential

Project result: The KLS conjecture.

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

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_HessianOperator
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_WeakHessian
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Alexandrov
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Caffarelli
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_GradientLipschitz
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_HessianRegularity
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Subgradient
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Viscosity
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_CEK_MomentMap
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_Isotropic
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/CEK/MomentRegularity/Potential.lean#L1-L324 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.CEK.MomentRegularity.Potential`, import-context bundle `KLSModular_FunctionalInequalities_KLS_CEK_MomentRegularity_Potential`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

View graph