arXiv:2607.28198v2 Announce Type: replace Abstract: Many dexterous manipulation tasks require the object to remain securely held throughout the interaction. From the perspective of hand-object relational motion, such manipulation comprises four canonical skills: grasping, relocation, in-hand rotation, and in-hand translation. Human hands flexibly compose these skills to accomplish complex tasks. Existing approaches, however, model these skills separately with skill-specific action constraints, objectives, or even dedicated hand morphologies, which breaks the compatibility and continuity required for long-horizon composition. In this work, we present a unified framework that models all four skills in a single formulation that shares the same state and action spaces and a common objective structure. This formulation enables distillation of a single cross-skill policy conditioned on the relational motion objectives, which achieves strong performance across all four skills, generalizes to unseen objects, remains robust to disturbances, and chains skills into long-horizon manipulation without switching policies. The framework also transfers effectively across different hand morphologies. Overall, our results suggest that different dexterous manipulation skills can be viewed as instantiations of a shared task formulation, revealing the intrinsic consistency. Project page: https://zdchan.github.io/UniCross/