{
 "tm": "1RB0RF_1RC0RE_1LD1RA_1LA0LD_1RA---_0RA0LB",
 "bucket_reason": "Med confidence after the proof-prep stage. The rules and the cleanup time are exact, but non-halting needs one per-epoch inequality that is not proven yet.",
 "question": "R3's cleanup is now exact and safety reduces to one per-epoch inequality (2^P <= N, via L*), the same crossing arithmetic R2 is stuck on: fund one joint crossing-lemma stage, start Rocq on the exact rules, or park?",
 "options": [
  {
   "id": "crossing",
   "label": "One joint crossing-lemma stage with R2 (2 h, native)",
   "consequence": "Search natively for an inductive bound on the potential Y near powers of two, aimed at 2^P(e) <= N_e (2.3-bit margin) rather than L* (0.32 bits). Possible route: a scale-invariant crossing automaton. Stop rule: if nothing inductive appears, park R2 and R3 together."
  },
  {
   "id": "rocq",
   "label": "Start the Rocq model of the exact rules now",
   "consequence": "Formalize the token hub, the inc recursion, E/B0/B1 and the cleanup formula. That work is reusable whatever the bound turns out to be, but the final theorem stays blocked on L* (or its replacement)."
  },
  {
   "id": "park",
   "label": "Park R3 with R2 until a crossing idea appears",
   "consequence": "No more agent time now. The exact model and the open inequality are recorded in notes.md and deepen.json."
  }
 ],
 "recommended": "crossing",
 "rationale": [
  "All rules are exact and validated (11,584 reachable words, all 192,042 R1 steps to 1e9, 100,000 epochs).",
  "What is left is one inequality, the same crossing loop as R2's R1, so one stage serves both machines.",
  "Target 2^P <= N directly: it keeps a 2.3-bit margin, while L* falls to 0.32 bits."
 ],
 "evidence": [
  {
   "kind": "figure",
   "text": "Hub rows: gap and counter over four epochs",
   "href": "img/hubs_counter_epochs.png"
  },
  {
   "kind": "fact",
   "text": "Token R1 matches the TM on 11,584/11,584 reachable marked words and all 192,042 R1 steps from blank to 1e9.",
   "href": "scripts/prep/lockstep_1e9.txt"
  },
  {
   "kind": "fact",
   "text": "Cleanup at exactly 2^P, P = zeros of Y below the last j: 100,000/100,000 epochs and 240/240 direct-TM runs.",
   "href": "scripts/prep/invariants_1e5.txt"
  },
  {
   "kind": "fact",
   "text": "L* fails only at epochs 7, 8, 14 and 15 to N = 1.09e6, but its margin falls to 0.32 bits at N = 654,227.",
   "href": "notes.md"
  }
 ],
 "effort_if_yes": "About 2 h of agent time for the joint crossing stage, run natively with no Coq search.",
 "updated": "2026-10-10",
 "answer": {
  "option": "crossing",
  "note": "auto-applied: Claude's recommendation, under Dennis's standing instruction 'do your recommendations and continuously orchestrate' (2026-10-10, while he was away). Override any time.",
  "date": "2026-10-10"
 }
}