Donaldson–Scaduto conjecture on collapsing special Lagrangian submanifolds

Let $X$ be a Calabi–Yau $3$-fold with a K3-fibration $\pi:X\rightarrow Y$, let $\omega_X$ and $\omega_Y$ be Kähler forms on $X$ and $Y$, respectively, and let $\widetilde{\omega}_t$ be the unique Calabi–Yau metric in the Kähler class

$$[\omega_X]+\frac{1}{t}\pi^*[\omega_Y],$$

for $t\ll1$. Donaldson–Scaduto conjecture. If $L_t$ is a $1$-parameter family of special Lagrangian submanifolds with respect to $\widetilde{\omega}_t$, then $L_t$ Gromov–Hausdorff converges to a graph in $Y$ whose edges are geodesics of the specified quadratic-differential geometry, equivalently gradient-flow lines of a suitable area functional. The conjecture is presented as the Calabi–Yau, or $S^1$-reduced, counterpart of the original Donaldson–Scaduto conjecture for $G_2$-manifolds. Its general validity is not established in the supplied text.