{
 "tm": "1RB0RF_1RC0RE_1LD1RA_1LA0LD_1RA---_0RA0LB",
 "bucket_reason": "Med confidence after the crossing stage, whose stop rule fired. Non-halting now rests on one rare-event lemma (Big-Y) with no inductive proof.",
 "question": "The crossing stage hit its stop rule (Lemma S proven, the Big-Y lemma open, with 3 instances in 1e7 epochs): park R3 with R2, fund one Big-Y stage, or start Rocq with Big-Y as the one hypothesis?",
 "options": [
  {
   "id": "park",
   "label": "Park R3 with R2 (stop rule)",
   "consequence": "No more agent time now. The integer model, Lemma S and the open Big-Y lemma are recorded in notes.md and deepen.json. Revive when a crossing idea appears, for example from #29."
  },
  {
   "id": "bigy",
   "label": "One Big-Y stage (2 h, native)",
   "consequence": "Try to show that Y_e >= 2^(bitlen N_e + 1) happens only right after an exact-power epoch (Y = 2^m), by bounding the j weight at depth >= m-1. There C needs only popcount(N - v + 1) >= 2 - s. Stop rule: park if it does not close."
  },
  {
   "id": "rocq",
   "label": "Rocq model with Big-Y as the hypothesis",
   "consequence": "Formalize the token hub, the inc recursion, E/B0/B1, the cleanup and Lemma S. The final theorem stays conditional on the Big-Y lemma."
  }
 ],
 "recommended": "park",
 "rationale": [
  "Stop rule fired: no inductive form for C or C0; C0 breaks on random near-crossing states.",
  "Narrower gap than L*: Lemma S covers every epoch with Y < 2^(m+1); the rest occurs 3 times in 1e7.",
  "Big-Y has a concrete target, but it is the same crossing arithmetic that stalled R2."
 ],
 "evidence": [
  {
   "kind": "figure",
   "text": "Hub rows: gap and counter over four epochs",
   "href": "img/hubs_counter_epochs.png"
  },
  {
   "kind": "fact",
   "text": "Integer model to 1e7 epochs (N = 1.44e8): all safe, but the minimum margin is 1.000 bit (epoch 350,274, N = 2^22 - 4,693), not 2.3.",
   "href": "scripts/crossing/longrun_1e7.txt"
  },
  {
   "kind": "fact",
   "text": "Lemma S (C(e) => next epoch safe): 100,000/100,000 trajectory epochs and 59,887/59,887 random states.",
   "href": "scripts/crossing/lemma_s_checks.txt"
  },
  {
   "kind": "fact",
   "text": "Big-Y epochs (Y >= 2^(m+1)) to 1e7: only 9, 16 and 350,275, each right after a Y = 2^m pair; C-margins 3, 3, 15.",
   "href": "scripts/crossing/crossing_stats_1e7.txt"
  }
 ],
 "effort_if_yes": "Park: none. Big-Y: about 2 h of agent time, native, no Coq search. Rocq: several stages.",
 "updated": "2026-10-10",
 "answer": {
  "option": "park",
  "note": "Dennis: go with recommendations (2026-10-11)",
  "date": "2026-10-11"
 }
}