Reconstructing dynamic 3D scenes from monocular video requires inferring motion from noisy and intermittently visible observations. Long-range tracks provide valuable geometric constraints, but integrating their fragmented temporal coverage into shared, continuous motion remains challenging. We introduce RayCo4D, a ray-conditioned continuous motion model for monocular 4D reconstruction that explicitly separates visual measurements from latent 3D motion states. Each track is associated with a reference-time 3D query constrained to its camera ray, and its image and depth observations constrain shared latent motion nodes through local many-to-many associations. Each node maintains an $\mathrm{SE}(3)$ pose and body-frame velocity at sparse support times. A white-noise-on-acceleration process prior couples neighboring states and defines continuous-time interpolation, allowing observations across visibility intervals to jointly constrain the same latent state sequence. The inferred shared motion is transferred to Gaussian primitives through dual-quaternion blending, while reference-anchored local $\mathrm{SE}(3)$ residuals capture fine-scale non-rigid deformation beyond the shared scaffold. Experiments on diverse monocular dynamic scenes show that RayCo4D achieves competitive novel-view synthesis quality, improves structural and temporal consistency under rapid motion and incomplete tracks, and supports continuous-time rendering.

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