{
 "tm": "1RB---_0RC0RF_0RD0RA_1RE0LB_1LF0LE_1RC0LE",
 "bucket_reason": "Medium confidence after the carry stage: the time structure is exact (one chain per cycle at level t1(k xor c)), but the chain lengths above level 0 and the non-halting invariant are open, so proof.md waits.",
 "question": "W4-6 and its twin (line 612) now reduce to one chain per cycle at a known level: fund one more ~2 h stage for the chain-length law above level 0, try a wall-level closed-language search instead, or park?",
 "options": [
  {
   "id": "chain_law",
   "label": "Fund one ~2 h chain-length stage",
   "consequence": "Find what fixes the number of C walls in a level-q chain for q >= 1 (level 0 is an exact ruler), as a function of the lower levels' state; from it the wall windows and the invariant (gaps >= 0, zero gaps and the right end only in phase C). Stop rule: if no law fits all cycles to 1e11 in 2 h, both lines go to STUCK."
  },
  {
   "id": "wall_ctl",
   "label": "Wall-level closed-language search",
   "consequence": "Native search for a regular language over the pass/sweep machine at wall level (gap value, wall status S/O/C, head phase), closed under its steps; the complete A-tree makes the status pattern a plain binary counter. A hit is the invariant without the law; it may not close."
  },
  {
   "id": "park",
   "label": "Park both lines",
   "consequence": "No compute. Both lines go to STUCK with the exact model, the one-chain reduction and the level law kept for a later multi-level-counter method."
  }
 ],
 "recommended": "chain_law",
 "rationale": [
  "Each cycle is one chain from wall 2p+2, p = t1(k xor c): 0 mismatches, both lines.",
  "Level-0 chain lengths are an exact ruler; the same law above it would close (i)-(iii).",
  "One analysis serves 2 holdouts."
 ],
 "evidence": [
  {
   "kind": "figure",
   "text": "Fig 2: walls per cycle; each level wiggles half as often as the one before.",
   "href": "img/gapmap_1024.png"
  },
  {
   "kind": "fact",
   "text": "Level law p = t1(k xor c), c = 4672 (line 99) / 4673 (line 612): 0 mismatches for k >= 3,600.",
   "href": "data/levels_1e11.out"
  },
  {
   "kind": "fact",
   "text": "One-chain form = cycle map on every record of both lines and on 40,511 random words, 0 differ.",
   "href": "data/carry_random.out"
  },
  {
   "kind": "fact",
   "text": "Chain lengths: level 0 exact ruler; levels >= 1 geometric but no masked-ruler law.",
   "href": "data/chainlen_A.out"
  }
 ],
 "effort_if_yes": "~2 h agent time, light compute (all checks run on the stored 1e11 records in minutes).",
 "updated": "2026-10-12",
 "answer": {
  "option": "chain_law",
  "note": "Dennis: b (fund all five), 2026-10-12",
  "date": "2026-10-12"
 }
}