Moduli of Stokes torsors and singularities of differential equations

Let Ai be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol Ai be the solution complex of Ai. We prove that the good formal structure locus of Ai coincides with the locus where the restrictions to D of Sol Ai and Sol End Ai are local systems. Despite the very different natures of these loci (the first one is defined via algebra, and the second via analysis), the proof of their coincidence is geometric. It relies on moduli of Stokes torsors.