Gibbs polystability criterion for log Fano manifolds

Let $(X,\Delta)$ be a log Fano manifold. Gibbs polystability conjecture. $(X,\Delta)$ is Gibbs polystable if and only if it is uniformly Gibbs polystable if and only if it is K-polystable. This proposes equivalence between the probabilistic Gibbs notions and K-polystability for log Fano manifolds; the source provides no resolution.