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 },
 "decision": {
  "P1_met": true,
  "P2_met": true,
  "P3_smallest_size_all_20_seeds_men": 10000
 },
 "note": "The direct answer's gap is zero in expectation, not exactly: the two arms hold different lives once the shock changes who is born, so the direct gaps reported are sampling noise around zero."
}