Retargeting human demonstrations into dynamically feasible dexterous hand trajectories requires resolving complex contact physics, yet current methods either omit physical constraints or rely on computationally expensive sampling-based optimization in simulation. Reinforcement learning has previously been used to achieve planning and control through contact dynamics; however, standard policies require object-specific training and fail to generalize across arbitrary geometries. This work reframes physics-based retargeting as a residual learning problem, where we demonstrate that zero-shot generalization across objects relies on structured state representations. Specifically, formulating the observation space to include a localized contact-error signal guiding each robot link to its target coordinate on the object surface enables a single, unified residual policy to successfully grasp novel, unseen object geometries. Rolling out this policy in simulation on a kinematic reference trajectory yields a physics-based retargeter, OATH. Operating at 0.4 seconds of compute per second of reference, OATH achieves 2.4x faster-than-real-time performance and a 60-350x reduction in computational cost compared to sampling-based methods. The system recovers 58% of held-out and 54% of unseen-object DexYCB trajectories while maintaining a sub-2 cm tracking error.

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