The gait selector answers to incentives, not exploration

What each arm was

Both start from MotionLibWalk — the one configuration measured to walk (0.537 m/s at 98% tracking) — and change exactly one thing, per the discipline rule that six unattributable runs bought us.

Arm 1 (exploration). The gait logit's entropy bonus was paying the policy to keep the bit noisy at ~50/50 forever; the hypothesis was that this jitter prevented any committed gait sequence from ever being sampled long enough to show its value. Entropy on that dim zeroed, initial noise raised to √2: explore hard early, then commit. Verdict: p(bound) 0.010. Exploration was not the bottleneck.

Arm 2 (incentives). At the base's weight of −1, committing to pure trot costs 0.005/step against 0.042/step of earnable positives — pocket change, rationally ignored. At the paper's −15 (annealing to zero over the run, the schedule Table S3 specifies), ignoring the term forfeits more than everything else combined. Verdict: p(bound) 0.568. The selector works; it was just never worth using.

The numbers side by side

Sync numbers are Jaccard overlap of stance intervals per leg pair. A clean library trot would read diagonal ≈ 1.0, lateral ≈ 0. Nobody is there yet — but arm 1 is the first policy where diagonal clearly wins.

Why this isn't the final word

These are 1,500-iteration runs, and Table S3's own schedule anneals the gait terms over 50,000 epochs — every number above describes the first 3% of the curve, where the pressure has barely released. The budget run (MotionLibWalkLong: same −15, same anneal stretched to 15,000 iterations, commands widened to 0.0–1.5 m/s so bound can actually pay) has been running on server-gpu since tonight. The question it answers: does arm 2's limp heal as the anneal fades, the way the paper's design intends?

If WalkLong converges clean, the recipe is: arm 1's runner (clean trot imprint) + arm 2's weight (live selector) + budget. That combination is the candidate teacher for distillation.