Shear--Layer Structure in Galactic Rotation Curves

This record contains a derivative-based, model-independent analysis of galactic rotation curves using the angular frequency profile Ω(R)=V(R)/R and its first and second radial derivatives. The work introduces a purely kinematic method to detect and characterize regime transitions analogous to shear layers in fluid dynamics. The method is applied to the Milky Way, M31 (using two independent tracers), and to the SPARC galaxy sample. The paper demonstrates that disk galaxies exhibit an extended, geometrically well-defined transition region (a “shear layer”) that is distinct from the classical tracer-dependent break radius.