(Heuristic) If the derived category class of $L$ is semistable in Joyce’s sense, then we can choose an optimal representative which is a special Lagrangian, or at least has phase oscillation arbitrarily small. By conjecture 3.31, we cannot have any destabilizing distinguished triangle, i.e. $L$ is Thomas-Yau semistable.

Conversely, if $L$ is not a semistable object in Joyce’s sense, then from its Harder-Narasimhan decomposition we can produce a destabilizing distinguished triangle $L_{1}\to L\to L_{2}\to L_{1}[1]$, with almost calibrated $L_{1},L_{2}$, which violates Thomas-Yau semistability. ∎