Tian's coercivity conjecture for cscK metrics

Let $(X,\omega)$ be a Kähler manifold, and let the Mabuchi functional be the functional on the space of Kähler metrics in the fixed Kähler class represented by $\omega$. Tian's conjecture. The manifold $(X,\omega)$ admits a cscK metric if and only if the Mabuchi functional is coercive. Tian's refinement strengthens Mabuchi's bounded-below condition to coercivity; the source does not state its resolution.