Convex-hull conjecture for almost toric fibrations

Let $M$ be a symplectic manifold with an almost toric fibration (ATF), and let an almost toric base diagram (ATBD) describe it. Assume the cuts of the ATBD lie inside the eigenline of the respective node, and let $L$ be a monotone Lagrangian fiber. The boundary Maslov-2 convex hull conjecture. The boundary Maslov-2 convex hull of $L$ is determined by the limit orbifold; specifically, its vertices should be the primitive vectors describing the fan of the limit orbifold. This would relate the disk-counting data of monotone Lagrangian fibers to the toric geometry of the limiting orbifold. The paper presents this as a conjectural consequence of expected wall-crossing behavior, and no proof or resolution is supplied.