Yang's BC-positivity characterization conjecture

Let $X$ be a compact Kähler manifold, let $T_X$ denote its holomorphic tangent bundle, and let BC-1 positivity refer to the paper's curvature-positivity notion for $T_X$. Yang's conjecture. The manifold $X$ is rationally connected if and only if $T_X$ is BC-1 positive. The paper establishes related sufficient conditions, including rational connectedness from BC-$p$ positivity for every $1\leq p\leq \dim X$, but does not resolve this equivalence.