{
 "what": "The numbers behind the per-task tail figure on /backup/curve (public/backup/default-curve.json): one row per task, and the configuration that recomputes the receipt's p, worst-5 % shares and null band from this file alone.",
 "unit": "one task: a prompt to the commit it produced, or one headless-runner verdict row (a dispatched spec row to the commit it graded)",
 "tokens": "input + cache_create + cache_read, summed over every model call in the task",
 "fields": {
  "task": "a per-export index: the row's position in the draw order (file order), derived from no key",
  "arm": "steer = a scope declared before the work; plain = none",
  "decile": "complexity decile 0-9 (see decile)",
  "tokens": "total tokens of the task (see tokens)"
 },
 "order": "rows are in the record's order; the redraws index into it, so the order is load-bearing — filter by arm and decile, never re-sort",
 "arm_sha256": {
  "key": "session:sha",
  "steer": "a555fcd4a2e7f0e1b12fbf9f3fb44a7b9857eed77def48725d475ef0b9cf9912",
  "plain": "104b188c139c3348a2a0175d10cc09e95b54b967c1402e0a8e8fb235a35c3b6c",
  "how": "sha256 over the sorted session:sha keys of each arm, as the receipt and the page stamp it; the keys themselves are not exported"
 },
 "n": {
  "steer": 44,
  "plain": 598
 },
 "seed": 7,
 "sims": 20000,
 "level": 0.95,
 "grid": 96,
 "lcg": {
  "multiplier": 1103515245,
  "increment": 12345,
  "modulus": 4294967296,
  "rule": "s ← (multiplier × s + increment) mod 2^32, starting from s = seed; each call returns s ÷ 2^32 (a float64 in [0, 1)). The product must be taken exactly mod 2^32 (in float64 languages split s into 16-bit halves)."
 },
 "decile": "complexity = log2(1 + files) + log2(1 + insertions + deletions) + log2(1 + dirs) + off_pct / 25 — files, lines, dirs from `git show --numstat`; off_pct the flight tape commit row's delta.offPct (the one Rust walk), 0 when the walk has not landed; percentile mid-rank over ALL units (both labels), ties count half; decile = min(9, floor(pct / 10))",
 "statistics": {
  "p": "the declared tasks are taken in file order, keeping those whose decile has at least one undeclared task. For each of `sims` redraws: for each kept declared task, u = next LCG value, draw the undeclared task at index floor(u × m) (0-based) of the m undeclared tasks in that decile, in file order; add up the draws. p = (redraws whose sum ≤ the kept declared tasks' sum) ÷ sims. One-sided: a small p says the declared total is smaller than chance at the same complexity.",
  "worst5_share": "per arm: sort the tokens descending, k = ceil(0.05 × n), share = (sum of the top k) ÷ (sum of all n). Over every task of the arm.",
  "null_band": "grid: a = log10(min tokens), b = log10(max tokens) over both arms; x_g = floor(10^(a + (b − a) × g ÷ (grid − 1)) + 0.5) for g = 0 … grid − 1. The SAME redraws as p, in the same order: for each redraw and each x_g, c = count of drawn tasks ≥ x_g. tail = (1 − level) ÷ 2 computed in float64 (0.025000000000000022, so tail × sims = 500.00000000000045 and the lower edge is the 501st smallest c). lo_k = the smallest c such that the number of redraws with count ≤ c is ≥ tail × sims; hi_k the same at (1 − tail) × sims. The band is lo_k ÷ n and hi_k ÷ n, n = the kept declared tasks. The declared curve at x_g is (declared tasks ≥ x_g) ÷ n; below lo is BELOW THE NULL."
 },
 "receipt": {
  "path": "public/backup/default-curve.json",
  "at": "2026-10-05T02:44:56.873Z",
  "p": 0.00485,
  "worst5_share": {
   "steer": 0.17034375576715438,
   "plain": 0.3871655456215317
  },
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 "reference": {
  "python": "/backup/actuarial-dataset.py",
  "r": "/backup/actuarial-dataset.R",
  "csv": "/backup/actuarial-dataset.csv"
 },
 "not_sufficient_for": "whether a declared task did the same work as an undeclared one (most declared tasks ran unattended, so route and scope are confounded); whether any of the work was good (Rice)",
 "tasks": [
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  {"task":1,"arm":"plain","decile":7,"tokens":12720650},
  {"task":2,"arm":"plain","decile":6,"tokens":3406197},
  {"task":3,"arm":"plain","decile":9,"tokens":77674538},
  {"task":4,"arm":"plain","decile":6,"tokens":2768214},
  {"task":5,"arm":"plain","decile":9,"tokens":1302657},
  {"task":6,"arm":"plain","decile":9,"tokens":15216696},
  {"task":7,"arm":"plain","decile":3,"tokens":2536512},
  {"task":8,"arm":"plain","decile":1,"tokens":774836},
  {"task":9,"arm":"plain","decile":9,"tokens":10534748},
  {"task":10,"arm":"plain","decile":4,"tokens":1252402},
  {"task":11,"arm":"plain","decile":9,"tokens":5461802},
  {"task":12,"arm":"plain","decile":7,"tokens":11250418},
  {"task":13,"arm":"plain","decile":7,"tokens":9930220},
  {"task":14,"arm":"plain","decile":2,"tokens":4261667},
  {"task":15,"arm":"plain","decile":1,"tokens":9299768},
  {"task":16,"arm":"plain","decile":6,"tokens":6443890},
  {"task":17,"arm":"plain","decile":6,"tokens":1049324},
  {"task":18,"arm":"plain","decile":5,"tokens":5943369},
  {"task":19,"arm":"plain","decile":1,"tokens":879430},
  {"task":20,"arm":"plain","decile":1,"tokens":1528230},
  {"task":21,"arm":"plain","decile":3,"tokens":4322540},
  {"task":22,"arm":"plain","decile":1,"tokens":2158534},
  {"task":23,"arm":"plain","decile":2,"tokens":3439777},
  {"task":24,"arm":"plain","decile":4,"tokens":7991172},
  {"task":25,"arm":"plain","decile":1,"tokens":1787237},
  {"task":26,"arm":"plain","decile":3,"tokens":6605796},
  {"task":27,"arm":"plain","decile":5,"tokens":12732611},
  {"task":28,"arm":"plain","decile":2,"tokens":4846453},
  {"task":29,"arm":"plain","decile":6,"tokens":9316235},
  {"task":30,"arm":"plain","decile":5,"tokens":9664779},
  {"task":31,"arm":"plain","decile":2,"tokens":1805513},
  {"task":32,"arm":"plain","decile":9,"tokens":3007170},
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  {"task":34,"arm":"plain","decile":8,"tokens":14984220},
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  {"task":41,"arm":"plain","decile":3,"tokens":638005},
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