There is a micro-local version of Riemann-Hilbert correspondence over nodal curve $X$ given by Roman Bezrukavnikov Mikhail Kapranov in the paper: Micro-local sheaves and quiver varieties
The de Rham side of the Riemann-Hilbert correspondence is the category of $de\ Rham\ microlocal\ sheaves$. The definition of $de\ Rham\ microlocal\ sheaves$ is defined as follows:
My Question is: Is there a geometric meaning (origin) for the back and forth morphisms $u_x, v_x$ in above definition? Why is this kind of definition the "right one" for Riemann Hilbert correspondence?
