The Kähler uniruledness and positive scalar curvature conjecture

Let $X$ be a compact Kähler manifold. Say that $X$ is uniruled if it is covered by rational curves, and let a smooth Kähler metric mean a smooth positive Kähler form on $X$. Kähler positive scalar curvature conjecture. $X$ is uniruled if and only if $X$ admits a smooth Kähler metric with positive total scalar curvature. This is presented as a conjecture of particular interest in Kähler geometry. The source gives no resolution in the stated generality; it notes related equivalences for Moishezon manifolds via the preceding conjecture and an external result.