Mean curvature flow convergence conjecture for low-oscillation exact Lagrangians

Let $(M,\omega,\Phi)$ be a Calabi–Yau $n$-fold, and let $\eta$ be an $n$-dimensional homology class in $M$. For an oriented exact Lagrangian $L$ in $M$, write

$$\operatorname{osc}(L)=\max(\theta)-\min(\theta),$$

where $\theta:L\to\mathbb{R}$ is its phase function. Mean curvature flow convergence conjecture. There is a constant $c>0$ such that, for every oriented exact Lagrangian $L$ in $M$ with $\operatorname{osc}(L)<c$, the mean curvature flow of $L$ converges smoothly.

The conjecture concerns the persistence and regularity of exact Lagrangians whose phase has small oscillation. The supplied text does not specify the limiting object or provide evidence that the conjecture has been resolved.