# Continuous refinement after the coarse search

The original 2,040-pose grid has spatially feasible poses at every frame, but no path meeting 0.5 m/s throughout the second source segment. Its 2.5 cm height spacing exceeds the 2.083 cm allowed per 24 fps interval. The provisional support/swing transitions also introduce foot-correction discontinuities. Preserve the coarse candidates and selection; do not relax any acceptance limit.

Add continuous trajectory proposals. For each source segment and constant depth represented by feasible coarse candidates at every frame, solve for body Z and two foot correction Z trajectories together. Body bounds are the minimum and maximum feasible coarse heights at each frame. During provisional swing the foot correction equals body correction. During provisional support its allowed band is the measured source-preserving correction ±1.5 cm, within the existing 2 cm clearance limit. IK must still reproduce each chosen target within 2 mm. Constrain adjacent body/foot correction changes to 0.018 m (0.432 m/s), leaving numerical margin below the existing 0.5 m/s gate.

Use SciPy SLSQP with a quadratic cost on body offset, foot-to-body correction, and between-frame correction variation. This is a standard numerical method, not a novel solver claim. Re-evaluate every proposal through the actual rig, ground probes, leg lengths, and visibility. Nonconvex visibility and rig behavior can reject a numerical proposal. Add only measured proposals to the original per-frame candidate sets; both framewise and coordinated selectors receive exactly the same expanded sets. Existing hard acceptance thresholds and source segmentation remain unchanged.

This refinement is post-hoc development, not preregistered or held-out validation. The original coarse-only selection is retained as evidence.