The uniruledness conjecture via Kodaira dimension and RC-positivity

Let $X$ be a projective manifold, let $K_X$ be its canonical bundle, let $K_X^{-1}$ be its anticanonical bundle, and let $\kappa(X)$ denote its Kodaira dimension. Uniruledness conjecture. The condition $\kappa(X)=-\infty$ is equivalent to each of the following: $X$ is uniruled; $K_X$ is not pseudo-effective; $K_X^{-1}$ is RC-positive; $X$ admits a Hermitian metric with positive Chern scalar curvature; and, for every ample line bundle $A$, there is a positive integer $c_A$ such that

$$H^0(X,K_X^{\otimes \ell}\otimes A^{\otimes k})=0$$

whenever $\ell\geq c_A(k+1)$ and $k\geq 0$. The source notes that the equivalence of uniruledness with non-pseudo-effectivity of $K_X$ is already known, but presents the full equivalence as a conjectural formulation.