Smoothness Ranks Skill, Not Success: An Audit of Published Trajectory-Smoothness Curation Metrics Under Episode-Length Controls

Trajectory smoothness has been proposed as a cheap, training-free signal for curating imitation-learning demonstrations, most recently by rinse, which introduces Spectral Arc Length (SAL) and a contact-aware Trajectory-Envelope Distance (TED). We test whether these published metrics survive episode-length controls on real robomimic data. On can/mh, SAL separates better from worse operators with AUROC 0.952, but episode length alone achieves 0.957, and inside a duration-matched band SAL falls to 0.628 while raw mean jerk, the baseline rinse argues against, rises to 0.896. The confound replicates on square/mh. On can/mg, where every episode is exactly 150 steps, SAL is at chance (0.454) and TED is inverted (0.376) against task success, while jerk reaches 0.706. Training GMM behavior-cloning policies on each metric's curated subset (10 seeds), curating by TED costs roughly a third of downstream success relative to random selection of the same size (0.240 vs. 0.360, p=0.0001, surviving Bonferroni correction), while SAL and jerk are indistinguishable from not curating. Under a diffusion policy TED still ranks worst, though its deficit is not resolvable at five seeds, and jerk becomes significantly better than both baselines, so the curation decision does not transfer unchanged across the two policy configurations we tested. Inspecting trajectories shows why TED inverts: successful manipulation requires sustained high-deviation motion through contact, while failure is low-amplitude hovering that a smoothed envelope follows closely.