Isomonodromic Derivative-Order Geometry: Zero-Curvature Ladder Flows, Singular-Velocity Fingerprints, and Exact Deformation Recovery

This preprint develops the isomonodromic face of derivative-order geometry by introducing mixed derivative–deformation ladders and zero‑curvature ladder flows. It proves projective Lax covariance and derives singular‑velocity fingerprints for moving singularities. The work shows that finite windows determine the deformation exactly, giving a complete recovery theorem for isomonodromic derivative‑order ladders.