The SYZ conjecture on special Lagrangian fibrations

Let $f\colon\mathcal{X}^*\to\Delta^*=\{t\in\mathbb{C}\mid 0<|t|<1\}$ be a flat proper family that is a maximal degeneration, meaning that its monodromy has maximal unipotency index. Let $\mathcal{L}^*$ be a relatively ample line bundle, and let $g_{\rm KE}(\mathcal{X}_t)$ be the family of Ricci-flat Kähler metrics on $\mathcal{X}_t$ for $t\neq 0$, with Kähler classes $c_1(\mathcal{L}_t)$, where $\mathcal{L}_t:=\mathcal{L}|_{\mathcal{X}_t}$. The SYZ conjecture on special Lagrangian fibrations. For any $|t|\ll 1$, there is a special Lagrangian fibration on $\mathcal{X}_t$ with respect to a certain meromorphic relative section of $K_{\mathcal{X}^*/\Delta^*}$. This is the special Lagrangian-fibration prediction associated with large complex structure limits and mirror symmetry; the paper states in its abstract that the Kontsevich–Soibelman conjecture is solved at an enhanced level for finite quotients of abelian varieties, but the supplied text does not establish that this full general statement is resolved.