Universal minimal-entropy conjecture for 2-fold branched covers of links

For a link $L$ in $S^3$, let $M_L\to S^3$ be the $2$-fold branched cover branched over $L$. The quantity $\ell_g(M_L)$ denotes the minimal entropy associated with $M_L$. Universal minimal-entropy conjecture. For any link $L$ in $S^3$, we have

$$\ell_g(M_L)\asymp \dfrac{1}{g}.$$

The preceding results establish this behavior for infinitely many links, including links whose branched covers give non-hyperbolic and hyperbolic $3$-manifolds, but the assertion for every link remains open.