arXiv:2609.18117v3 Announce Type: replace Abstract: Dexterous grasp synthesis has advanced rapidly in generating stable and physically plausible hand poses, but real-world manipulation requires grasps that preserve the function implied by the task. We study open-vocabulary task-oriented dexterous grasp generation, where a robot must infer functional intent from free-form language, ground it in multi-view visual observations and object geometry, and generate an executable high-degree-of-freedom grasp. We present OpenDexGrasp, a unified data and generative modeling framework for this setting. OpenDexVerse provides dual-source supervision organized by the Coverage-to-Alignment (C2A) Recipe: OpenDex-Scale offers large-scale semantic and geometric coverage through automatic grasp synthesis and vision-language annotation, while OpenDex-Align supplies high-quality embodied alignment through human teleoperation and category-level transfer. OpenDexGrasp learns a shared perception-action latent representation that couples open-vocabulary vision-language context with dexterous action generation. Affordance grounding and grasp generation provide complementary supervision over this latent space, enabling direct generation of task-consistent dexterous grasps without a separate affordance-to-pose inference stage. Extensive simulation and real-robot experiments demonstrate improved functional alignment, physical feasibility, generalization to unseen categories, and real-world execution success. Additional details and videos are available at https://opendexgrasp.github.io/.