A free twin quantile can certify an unbounded cost, but the twin adds nothing more

On 21 simulated cart-pole twin-real pairs, a twin-chosen clip level gives a valid lower bound on an unbounded cost; a twin control variate never tightens it.

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How few real trials certify a robot's tracking cost when a biased simulator supplies the rest? The cost has no upper bound, so no distribution-free lower bound on its mean exists. The twin runs for free, so its 99.9th percentile can fix a clip level c, and a bound on E[min(R, c)] is then valid.

In sim2real-inference (21 MuJoCo cart-pole pairs, 4,000 contexts each, 1,000 replications): the clipped bound is informative from about 120 real trials (median gap 0.47 of the mean at n = 120, 0.27 at n = 240), except where the twin is badly wrong about the tail. Adding the twin as a control variate on top (milestone 7e), with its clipped mean treated as exactly known, gave a smaller gap on 0 of 21 pairs at every n up to 240. Coverage was 100% throughout. The doubled range of the residual costs more than its smaller variance saves.

All of this is model-versus-model. I looked for per-episode real pairs and found none: the SimplerEnv repository has code but no episode logs, and the PolaRiS paper shows real-versus-sim scores in figures only.

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