{
 "tm": "1RB0RA_1RC0RD_1RD0LC_1LE1RA_---1LF_1RB0LC",
 "bucket_reason": "med confidence after grammar2: the abstract simulator matches every marker turn to 1e9 with validated rules, but no invariant yet excludes the unsupported (possibly halting) cases",
 "question": "The digit-level simulator now matches all 227,414 marker turns to 1e9 with validated rules: fund an invariant stage that shows the unsupported cases never occur (then proof.md), or park W4-7 and 707?",
 "options": [
  {
   "id": "invariant",
   "label": "Invariant stage (about 2-3 h)",
   "consequence": "Find a property of digit lists that is closed under the rules and excludes the two unsupported cases (ready field 2 at a left visit; B> into a ready (0,0) followed by the wrong digit). Check it natively along the orbit and on random lists. Stop rule: park if no small invariant closes. Then proof.md, then Rocq."
  },
  {
   "id": "park",
   "label": "Park W4-7 (and 707)",
   "consequence": "No further cost now. Rules, abstract simulator and all checks stay in scripts/grammar/ for reuse."
  }
 ],
 "recommended": "invariant",
 "rationale": [
  "Stop rule did not fire: the 111/1111 tops were a parser artifact; all 227,415 turns parse in the 6 encodings.",
  "New B> rules validated: 19,907/19,907 op-level and 1,405/1,405 pass-level random instances, 0 failures.",
  "Orbit exact from step 10 to 1e9; the risky ready (0,0) pattern occurs only at the counter's top."
 ],
 "evidence": [
  {
   "kind": "figure",
   "text": "Fig 3: records from start A (ours): the nested fields show as streaks",
   "href": "img/records_1e8.png"
  },
  {
   "kind": "fact",
   "text": "absim2: 227,414/227,414 bell-1 marker turns exact from step 10 to 1e9, 667 left visits",
   "href": "data/absim2_orbit_check_1e9.json"
  },
  {
   "kind": "fact",
   "text": "Random instances: op level 19,907/19,907; pass level 1,405/1,405 (840 H1); 0 failures",
   "href": "data/validation_grammar2_op20000.json"
  },
  {
   "kind": "fact",
   "text": "Ready (0,0) after a ready 2 occurs only at the top (587 turns, safe next digit)",
   "href": "data/grammar2_ready00_contexts_1e9.json"
  }
 ],
 "effort_if_yes": "about 2-3 h of agent time (light simulation, no Coq); proof.md and Rocq are later stages",
 "updated": "2026-10-12",
 "answer": {
  "option": "invariant",
  "note": "Dennis 2026-10-12: 'Invariant stage'",
  "date": "2026-10-12"
 }
}