Sweep a cascade's gate and find the frontier

Model each record by three facts: is the cheap extraction wrong, would the strong model be wrong if escalated, and the verifier's probability that the cheap answer is wrong. cascade_metrics() escalates when that probability exceeds the threshold and counts escalation rate, recall, false alarms, cost, error and latency from the records themselves, so the lesson's formulas become something you check rather than assume. The sweep then shows the frontier on synthetic, overlapping verifier scores.