The $\mu$-semistability condition can be recast in terms of the central charge $Z(E)=-deg(E)+\sqrt{-1}rk(E)$, as saying $\arg Z(E^{\prime})\leq\arg Z(E)$ for all nonzero proper subsheaves $E^{\prime}\subset E$. It is worth emphasizing that except for the case of Riemann surfaces, $\mu$-stability does not give rise to a Bridgeland stability condition on $D^{b}Coh(X^{\vee})$, since skyscrapper sheaves will generally have zero rank and zero degree, hence zero central charge. A similar but more subtle failure of Bridgeland stability happens in the context of the deformed Hermitian-Yang-Mills connections (cf. [18, section 4]). Such a failure does not spell doom for the PDE applications, nor for DT theoretic applications.²⁴²⁴ 24 R. Thomas defined DT invariants for $\mu$-stability long before the insight of Bridgeland. Even though Bridgeland stability seems to be a plausible framework for special Lagrangians in the light of Joyce’s proposal, it is probably advisable to maintain a more flexible attitude to stability conditions.