Deterministic Neighborhood Rotation (DNR) for Categorical Variables in Derivative-Free Optimization

Version 2 (major revision). This version replaces the previous file and contains the correct and updated manuscript. The theoretical positioning has been clarified as a finite-domain deterministic framework for categorical variables. The paper introduces deterministic neighborhood rotation (DNR), a fully deterministic and reproducible mechanism for exploring categorical variables without imposing artificial geometry. The logical structure has been strengthened, clearly separating exploration guarantees from algorithmic certification, and the numerical experiments have been significantly expanded. This version supersedes the previous preprint and should be considered the definitive version for citation.