RLF conjecture for isotropic divisors on projective irreducible holomorphic symplectic manifolds

Let $X$ be a projective irreducible holomorphic symplectic (IHS) manifold and let $D$ be an integral divisor on $X$ that is isotropic with respect to the Beauville–Bogomolov–Fujiki form, with $[D] \in \overline{\operatorname{Mov}(X)}$. RLF conjecture. The line bundle $\mathscr{O}_X(D)$ induces a rational Lagrangian fibration: there exists a birational map

$$f\colon X \dashrightarrow X'$$

where $X'$ is another projective IHS manifold, such that $f_*\mathscr{O}_X(D)$ induces a fibration, namely a surjective morphism with connected fibers,

$$X' \twoheadrightarrow B$$

to a projective base $B$ of dimension $\dim(X)/2$. The conjecture is known for all currently known deformation classes of projective IHS manifolds, but is not known in general.