Auroux's boundary conjecture for special Lagrangian torus fibrations

Let $X$ be a variety with a smooth anticanonical divisor $D$, set $U=X\setminus D$, and let $\pi:U\to B$ be a special Lagrangian torus fibration, meaning that its smooth fibers are special Lagrangian tori. Auroux's boundary conjecture. Near the divisor $D$, the special Lagrangian torus fibers of $\pi$ are $S^1$-bundles over a special Lagrangian torus fiber of a special Lagrangian torus fibration on $D$. This describes the expected boundary behavior underlying the SYZ construction of the mirror and is attributed in the source to Auroux's Conjecture 7.3.