Prove2Me

Import context: KLS/LogConcave/HessianTrace

Definition
KLSModular_FunctionalInequalities_KLS_LogConcave_HessianTrace

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.HessianTrace 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.WeakBrascampLieb, FunctionalInequalities.Analysis.Matrix.WeakDerivative, FunctionalInequalities.Analysis.Matrix.Trace.Algebra, and FunctionalInequalities.Probability.Moments. It also directly imports the external prerequisite modules Mathlib.Analysis.Matrix.Order and Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic.

Original module imports

import FunctionalInequalities.KLS.LogConcave.WeakBrascampLieb
import FunctionalInequalities.Analysis.Matrix.WeakDerivative
import FunctionalInequalities.Analysis.Matrix.Trace.Algebra
import FunctionalInequalities.Probability.Moments
import Mathlib.Analysis.Matrix.Order
import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic

Module navigation

Direct project imports: KLS/LogConcave/WeakBrascampLieb, Analysis/Matrix/WeakDerivative, Analysis/Matrix/Trace/Algebra, Probability/Moments.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.KLS.LogConcave.HessianTrace · Frozen source 408915f.

Definition code
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_WeakBrascampLieb
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_WeakDerivative
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_Trace_Algebra
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Moments
import Mathlib.Analysis.Matrix.Order
import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/KLS/LogConcave/HessianTrace.lean#L1-L292 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.LogConcave.HessianTrace`, import-context bundle `KLSModular_FunctionalInequalities_KLS_LogConcave_HessianTrace`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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