Thomas's existence and stability conjecture for special Lagrangians

Let $(X,\omega,\Omega)$ be a Calabi--Yau manifold and let $L$ be a compact zero Maslov Lagrangian in it. A Lagrangian is stable when it satisfies the stability condition under discussion for its Hamiltonian isotopy class. Thomas's conjecture. A special Lagrangian exists in the Hamiltonian isotopy class of $L$ if and only if $L$ is stable; when it exists, it is unique. This conjecture seeks a stability-theoretic criterion for the existence and uniqueness of special Lagrangian representatives, but the supplied text does not specify the stability condition or give evidence that the conjecture has been resolved.