Haiden–Katzarkov–Kontsevich–Pandit conjecture for Lagrangian mean curvature flow

Let $(X,\omega,\Omega)$ be a compact Calabi–Yau manifold, and let $L_1,\dots,L_r$ be special Lagrangian submanifolds in $X$ with the same phase that intersect transversely. Let $L=L_1\#\cdots\#L_r$ be obtained by performing Lagrangian surgery near the intersection points. Haiden–Katzarkov–Kontsevich–Pandit conjecture. The asymptotics of the Lagrangian mean curvature flow with initial condition $L$ are given by sums of iterated logarithms. This is a semistable geometric analogue of the Thomas–Yau picture; exponential convergence is known when $r=1$, and estimates are known for an example with $r=2$, but the stated general asymptotic description remains open.