Fukaya–Seidel–Smith's extremal-torus conjecture for ellipsoids

Let $0<a_1\le a_2\le\cdots\le a_n<\infty$, and let $E^{2n}(a_1,\dots,a_n)$ be the corresponding ellipsoid with standard symplectic form $\omega_{\mathrm{std}}$. A Lagrangian torus is extremal when its minimal symplectic area equals the Cieliebak–Mohnke capacity of the ambient symplectic manifold. Fukaya–Seidel–Smith's extremal-torus conjecture. Every extremal Lagrangian torus in $(E^{2n}(a_1,\dots,a_n),\omega_{\mathrm{std}})$ is contained entirely in the boundary $\partial E^{2n}(a_1,\dots,a_n)$. The source attributes this conjecture to the work cited as sfe; the supplied text does not state that it has been resolved.