Although it is unclear how to make sense of the intrinsic distance on a general Lagrangian integral current, mildly singular Lagrangians (for instance with local conical singularities) do have a sensible notion of intrinsic distance, and the arguments in this section extend practically to all non-pathological examples, covering all Lagrangians that appear in Joyce’s LMCF program. Furthermore, the potential clustering is robust under limits (cf. Cor. 5.9). As such, we believe it holds for all Lagrangians relevant to our variational program (cf. the class $\mathcal{L}$ in section 5.3 below).