Berman's Gibbs stability criterion for Fano varieties

Let $X$ be a Fano variety, and let $b3(X)$ denote the Gibbs stability invariant. Recall that K-stability and K-semistability are algebraic stability conditions for Fano varieties. Berman's conjecture. For a Fano variety $X$, $b3(X)>1$ if and only if $X$ is K-stable, and $b3(X)\geq 1$ if and only if $X$ is K-semistable. The conjecture would identify the probabilistic Gibbs stability invariant with the algebraic K-stability threshold and is not known for Fano varieties in general.