Donaldson–Scaduto conjecture on collapsing special Lagrangians

Let $X_t$ be a $1$-parameter family of compact Calabi–Yau manifolds with metrics $g_t$ admitting special Lagrangian fibration structures and with bounded diameters, and let $C_t$ be a holomorphic curve in $X_t$. Assume that $X_t$ are collapsing, meaning

$$(X_i,g_i)\xrightarrow{GH}(B_{\infty},g_{\infty}),$$

where $B_{\infty}$ is an integral affine manifold equipped with a Hessian-type metric outside a codimension-two locus. Donaldson–Scaduto conjecture. The curves $C_t$ converge to a tropical curve on $B_{\infty}$. This folklore conjecture motivates the use of tropical geometry in collapsing Calabi–Yau manifolds. The paper says it has been proved only in specific settings, including algebraic curves in $(\mathbb{C}^*)^2$ with incidence relations and torus fiber bundles, and remains unresolved for compact $\operatorname{SU}(n)$-Calabi–Yau manifolds.