 Isomonodromic deformation

A parameter deformation preserves generalized monodromy data, including Stokes matrices and formal monodromy at irregular points. If normalized sectorial matrices have parameter-independent jumps, $B=Y_z{Y}^{-1}$ agrees across overlaps. Its finite singularities and growth at infinity determine it by complex analytic arguments. Compatibility of $Y_{\lambda }=AY$ and $Y_z=BY$ is precisely the displayed zero-curvature identity, obtained by differentiating both equations and subtracting.