Rigidity conjectures for sextic double solids with cA singularities

Let $X$ be a $\mathbb Q$-factorial sextic double solid, meaning a double cover of $\mathbb P^3$ branched over a sextic surface, with singularities of the indicated types. Sextic double-solid rigidity conjecture. If $X$ has only $cA_1$ and $cA_2$ singular points, then $X$ is birationally superrigid. If $X$ has only $cA_1$, $cA_2$, and $cA_3$ singular points, then $X$ is birationally rigid. The source places these claims after known non-rigidity results for sextic double solids with sufficiently severe singularities; it does not state that either assertion has been resolved.