Import context: Probability/Stein/QuadraticAction

Definition

KLSModular_FunctionalInequalities_Probability_Stein_QuadraticAction

by Lazyfill · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

functional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-contextprobability

This bundle retains the import context of the source module FunctionalInequalities.Probability.Stein.QuadraticAction 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.Matrix.Integral, FunctionalInequalities.Analysis.Operator.Coordinates, FunctionalInequalities.Probability.Stein.Kernel, FunctionalInequalities.Analysis.Matrix.Sign, and FunctionalInequalities.Analysis.Matrix.Trace.Algebra. It also directly imports the external prerequisite module Mathlib.Probability.Moments.Variance.

Original module imports

import FunctionalInequalities.Analysis.Matrix.Integral
import FunctionalInequalities.Analysis.Operator.Coordinates
import FunctionalInequalities.Probability.Stein.Kernel
import Mathlib.Probability.Moments.Variance
import FunctionalInequalities.Analysis.Matrix.Sign
import FunctionalInequalities.Analysis.Matrix.Trace.Algebra

Module navigation

Direct project imports: Analysis/Matrix/Integral, Analysis/Operator/Coordinates, Probability/Stein/Kernel, Analysis/Matrix/Sign, Analysis/Matrix/Trace/Algebra.

Theorems in source order:

sum_integral_spectral_noise_energy_le

Project result: The KLS conjecture.

Original module · FunctionalInequalities.Probability.Stein.QuadraticAction · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_Integral
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Operator_Coordinates
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Stein_Kernel
import Mathlib.Probability.Moments.Variance
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_Sign
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Matrix_Trace_Algebra

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Probability/Stein/QuadraticAction.lean#L1-L200 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Probability.Stein.QuadraticAction`, import-context bundle `KLSModular_FunctionalInequalities_Probability_Stein_QuadraticAction`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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