RC-positivity conjecture for ample vector bundles

Let $E$ be an ample vector bundle over a projective manifold $X$, and let $\operatorname{rank}(E)$ denote its rank. RC-positivity conjecture. There exists a smooth Hermitian metric $h$ on $E$ such that $(E^{\otimes k},h^{\otimes k})$ is RC-positive for every $k\geq 1$, and $(\Lambda^pE,\Lambda^ph)$ is RC-positive for every $1\leq p\leq \operatorname{rank}(E)$. The source says this conjecture can be implied by Griffiths' conjecture; its independent resolution status is not given.