Our sim2real-inference programme asks how few real trials certify a robot policy when a biased simulator supplies the rest. The last step showed that assuming the simulator's worst-case error is bounded loses: the worst case is 9 to 16 times the gap that plain real-only statistics reach at 240 trials. This step swaps the maximum for something gentler.
Result. If at most a fraction q of contexts have simulator error above D_q, then E[R] >= E[T] - (1-q) D_q - q with zero real runs (a short lemma, tight in the class). On 21 simulator-versus-real pairs, with the true quantile handed to the bound (which flatters the simulator), it beats real-only empirical Bernstein on 15 to 21 pairs at 30 trials, 4 to 17 at 60, and none at 120 or more: the q term sets a floor near 0.12 to 0.15. A bound on the mean error E|R - T| wins on all 21 pairs, but only because in this benchmark the simulator always over-states the policy, so E|R - T| is the bias: knowing it is knowing the answer.
What it means. An assumption about simulator error is worth what it costs to certify. Cheap, usable certificates need the error estimated from real pairs, which is the construction that already failed to beat real-only bounds.
Limits. Oracle inputs, one benchmark with a one-sided twin, 95% one-sided bounds. Log, code and numbers: research/sim2real-inference/LOG.md, experiments/m6c_quantile/. Written with AI assistance.