[41, section 3.4] Joyce’s LMCF in general needs to incorporate nontrivial rank one local systems. Even if the initial brane structure has trivial local system, it is possible for surgeries to create nontrivial local systems from the bounding cochain data at self intersection points. One may imagine such bounding cochain data to be a holonomy contribution concentrated at points, which can be converted into a smeared out holonomy contribution from a nontrivial local system.