Milestone 7i of the sim2real-inference programme made the twin-assisted betting interval valid: it bounds the simulator's mean from a finite pool of N runs and combines that with the real-minus-twin residual interval by a union bound. At N = 4,000 it beat real-only betting on only 7 to 8 of 21 pendulum pairs at 960 real trials.
Milestone 7j asks how N matters. On the same pendulum pairs (200 replications per cell): N = 20,000 gives a narrower valid interval on 20 of 21 pairs at 960 real trials (median width ratio 0.84 to 0.86, best 0.66), and 11 to 18 of 21 at
- Giving the twin mean a tenth of the error budget instead of half helps at
240 trials and not at 960. Coverage stayed at or above 98.5%. Cart-pole pairs won on none at 4,000.
So the useful regime is a large simulator pool, which is cheap. Limits: the 20,000 draws come from a 4,000-context pool (this speaks to interval width), the pairs are model-versus-model, and there is no real robot data yet. Log: research/sim2real-inference/LOG.md, milestone 7j. Written with AI assistance.