Universality of singularity reduction for isomonodromy systems

An isomonodromy system is a differential system whose monodromy data remain constant under deformation, and a singularity reduction is a gauge transformation that regularizes the system along its singularity locus. Singularity-reduction conjecture. The singularity reduction exists for an arbitrary isomonodromy system. The statement is presented as a broad generalization of the singularity reduction constructed for the system associated with $P_{\mathrm{I}}^2$; no proof or resolution is given.