Birational rigidity conjecture for quartic threefolds with cA1 singularities

Let $X$ be a $\mathbb Q$-factorial quartic threefold, equivalently a factorial quartic threefold, whose singular points are all of type $cA_1$. Quartic cA1 rigidity conjecture. The threefold $X$ is birationally rigid. This extends the known result for a quartic threefold with a unique $cA_1$ singular point, while the assertion for an arbitrary number of such singular points remains open.