Thomas-Yau's existence conjecture for special Lagrangians

Let $(X,\omega,\Omega)$ be an exact Calabi-Yau manifold, and let $L_0$ be a nontrivial unobstructed exact Lagrangian brane with quantitatively almost calibrated phase function. Let $D^bFuk(X)$ be the derived Fukaya category, and let Thomas-Yau semistability mean the semistability condition defined using destabilising distinguished triangles. Thomas-Yau existence conjecture. If the derived Fukaya class of $L_0$ is Thomas-Yau semistable, then there is a special Lagrangian representative in the same $D^bFuk(X)$ class, or in a weaker $S$-equivalence class. This is the central existence claim of the paper's interpretation of the Thomas-Yau conjecture; the source emphasizes that the required compactness, weak-regularity Floer theory, and categorical foundations are not yet available.