(Heuristic) The existence of a special Lagrangian representative should imply Thomas-Yau semistability (cf. Conjecture 3.31). By the Thomas-Yau existence conjecture 5.21 this implies the Solomon functional has a minimizer $L^{\prime}$, which must be a special Lagrangian. Then the Thomas-Yau uniqueness conjecture 5.24 implies $L=L^{\prime}$ as currents. ∎