Linking and hull containment conjecture for elliptic and hyperbolic components

Let $K_1$ be an elliptic component and $K_2$ a hyperbolic component of a link $L=K_1\cup K_2$, and let $M$ be the embedded manifold whose holomorphic hull is denoted by $\widehat{M}$. The linking number is $\ell k(K_1,K_2)$. Linking and hull containment conjecture. If

$$\ell k(K_1,K_2)\neq 0,$$

then

$$K_2\subset\widehat{M}.$$

If $\ell k(K_1,K_2)=0$, then

$$K_2\not\subset\widehat{M}.$$

This conjecture proposes that nonzero linking with an elliptic component forces the hyperbolic component into the holomorphic hull, whereas zero linking excludes it. The source provides no resolution status.