{
  "name": "path dependence at scale: does a change in who is born show up decades later in who finds a partner, and only clearly at scale?",
  "registered": "2026-10-05",
  "question": "A direct answer computes each life from its own chances. In the world, lives find partners among each other. For ten years more boys are born than girls. Thirty years later, does the world show fewer men and more women partnered than a world without the change, when the direct answer says nothing changes? At what population size does that difference become stable across seeds?",
  "scope": "A property of the engine, not a claim about any country. Death and birth rates are the UK 2019 tables used in the published trace. The partnership, separation and leaving-home rates are the trace's placeholders. The size of any effect depends on them; its existence and direction come from the matching rule.",
  "world": {
    "engine": "src/lifecourse/lives.ts Lives.step, unchanged: deaths, separations, births, departures, then partnerships matched within a place and five-year age band (men one band up allowed)",
    "start": "N lives, born uniformly over the 90 years before month 0, half women, 64 places, exactly as experiment/lives/trace.ts",
    "months": 600,
    "rates": "as experiment/lives/trace.ts",
    "arms": {
      "baseline": "share of boys at birth 0.512 throughout",
      "shock": "share of boys at birth 1.18/2.18 = 0.5413 for births in months 0-119, then 0.512; this is a sex ratio at birth of about 1.18, the level recorded in China in the 2000s"
    },
    "pairing": "both arms use the same seed, so they share every draw; they differ only where the shock changes a birth's sex and what follows from it"
  },
  "sizes": [1000, 10000, 100000, 1000000],
  "seeds": "20 per size: 20261005 + k, k = 0..19",
  "cohort": "lives born in months 0-119 and alive at month 480 (ages 30 to 40)",
  "outcomes": {
    "primary": "gap_men: in the cohort, the share of men who have ever been partnered (checked at the end of every month), shock minus baseline, in percentage points; likewise gap_women",
    "direct": "the direct answer for the same cohort: each life partners when its own partnership draw comes up, with no need for anyone to match; computed from the same hazards. Its gap between arms is zero by construction, because the sex of other lives does not enter any life's own chances. Reported for level and gap."
  },
  "predictions": {
    "P1": "at N = 1,000,000, gap_men is below zero in all 20 seeds, and gap_women above zero in all 20",
    "P2": "at N = 1,000, gap_men has the predicted sign in fewer than 18 of 20 seeds (not stable at small size)",
    "P3": "the smallest size at which gap_men has the predicted sign in all 20 seeds is reported, whatever it is"
  },
  "report": "every seed's gaps, per size: mean, standard deviation, seeds with the predicted sign; the direct answer's levels; births that could not be stored (capacity) per run, which must be zero",
  "decision": "P1 and P2 are scored as met or not met, as registered. No size, seed, cohort, month or outcome is changed after any result is read."
}