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An $O(4^{\log^* n})$ Bound for the KLS Constant
The Kannan--Lovász--Simonovits (KLS) conjecture asks whether every isotropic log-concave probability measure on $\mathbb R^n$ has a Cheeger constant bounded below by a universal positive constant. The best previous upper bound is $ψ_n\lesssim\log^{1/4}n$, due to Letwin [Let26]. We prove that $ψ_n\le
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