Embedded contact knot homology conjecture for links

Let $L$ be a link in a contact three-manifold $Y$, and let $\alpha$ be any contact form on $Y$ adapted to $L$. Denote by $ECK(L,Y,\alpha)$ and $\widehat{ECK}(L,Y,\alpha)$ the full and hat versions of embedded contact knot homology. Embedded contact knot homology conjecture for links. One should have

$$ECK(L,Y,\alpha)\cong HFK^{-}(L,Y),$$

and

$$\widehat{ECK}(L,Y,\alpha)\cong\widehat{HFK}(L,Y).$$

These are the link version of the proposed correspondence between embedded contact knot homology and knot Floer homology. The source does not state whether the conjecture has been resolved.