Rational trace discontinuities and irrational continuity for Kwapisz-like rotation sets

This record contains the PDF of the manuscript “Rational Trace Discontinuities and Irrational Continuity for Kwapisz-Like Rotation Sets.” The paper studies an explicit family of rotation sets associated with torus dynamics. It determines the exact one-sided Hausdorff traces at every rational parameter, proves continuity at every irrational parameter, and establishes strict jump discontinuities at every rational parameter. It also develops quantitative Hausdorff and area separation bounds, Diophantine regularity results, Liouville irregularity, and continued-fraction structure in the rational trace polygons. This version is deposited for open access, citation, and long-term preservation.