One-step text-to-image models enable training-free, inversion-free editing with only 1--2 network function evaluations (NFE), while ChordEdit stabilizes such edits through low-energy smoothing along sampling time. Applied independently to video frames, however, it produces temporal flicker and edit-strength drift. We introduce \textbf{ChordVideo}, which extends the same low-energy principle to video time through shared noise, motion-aligned causal aggregation of per-frame Chord fields, and an optional temporally smoothed proximal correction. We derive a warping-error bound that separates motion bias from stochastic flicker and predicts diminishing returns with larger temporal windows. On TGVE/DAVIS with two one-step backbones, ChordVideo reduces warping error by \textbf{78\%} and flicker by \textbf{49\%}, improves CLIP frame consistency by \textbf{9--10 points}, and increases background PSNR by about \textbf{1.5,dB}, while retaining \textbf{2 NFE/frame}. Compared with seven multi-step editors, it achieves competitive temporal consistency and source preservation using \textbf{10--60$\times$ fewer model steps per clip

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