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* claim: #5248 * feat(motion): regenerate kept traces when source inputs change * feat(motion): add a parametric Chebyshev trace demo * perf(joints): reuse face measurements across motion samples Face-centred joint origins called Body::faces on every solve, bypassing the reference-mesh reuse used for rigid placements. Share face measurements with unchanged model geometry at the existing tolerance, while guarding replaced bodies and applying offsets after the cached measurements. Cover repeated named/nearest-face solves, shape edits, retained snapshots and direct replacement with deterministic work counts. The 145-point Chebyshev dimension and range updates retain identical sampled and interpolated curves. * perf(naming): skip preparation for cached face names Both face lookup paths spawned fresh workers over every body even when their name cells were ready. Prepare only cold cells, with direct handling of zero or one cold body. Preserve the existing parallel naming path and all face selection semantics. Deterministic regressions cover repeated picked and unique-name lookups, misses, partial warmup, renames, snapshots and moved copies. Release Chebyshev medians fall from 859 to 50 ms for a dimension edit and 871 to 34 ms for a sweep edit; all 145 samples and interpolated points remain identical. Full cargo xtask ci passes with RUST_TEST_THREADS=4 and the existing local Windows validation overlays.