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Existing continuous space-time video super-resolution methods often infer motion from only two endpoint frames and model the two motion directions independently, making them vulnerable to ambiguous correspondence and inconsistent trajectories. We introduce a continuous STVSR framework that combines long-context encoding, continuous HR feature lifting, and an endpoint-anchored PixelSpline. Long-range observations provide more reliable endpoint representations, while continuous upsampling constructs detailed appearance features directly on the requested HR grid. PixelSpline explicitly models each pixel's motion as a single continuous trajectory shared by both endpoints. Using this trajectory, our method warps endpoint colors into a coarse intermediate frame and aligns the HR features for residual reconstruction. Experiments across spatial and temporal upsampling settings demonstrate that the proposed framework offers a favorable quality--efficiency trade-off.