{
 "tm": "1RB0LD_0RC---_0LD0RF_1LE1LD_0LA0RD_0RB1RA",
 "bucket_reason": "The funded proof stage ended parked by its stop rule. It found the real mechanism and a different, likely shorter proof route, which needs a new stage.",
 "question": "Fund a second proof stage for 693 by the closed-tape-language route (symbolic shape closure, no catch-up arithmetic), or park 693 and its twins 528, 310, 548?",
 "options": [
  {
   "id": "fund_closure",
   "label": "Fund stage 2: symbolic shape closure (693; twins after)",
   "consequence": "About 2 h, 1 light process. Build a shape explorer (literal cells, runs w^(>=m), a star over the counter digits), compute the closed family from the X0 shape, check that no step is A or F on 0 before 1, and turn each transition into a checked rule in proof.md. Stop rule: park if the explored shape set does not close or a spurious halt appears that needs arithmetic."
  },
  {
   "id": "park",
   "label": "Park all four",
   "consequence": "Costs nothing. proof.md (working version), the checker and the random-parameter scripts stay in 693's folder."
  }
 ],
 "recommended": "fund_closure",
 "rationale": [
  "Between records a 3-cell binary counter counts wall steps; 4 phase rules checked.",
  "620 random-parameter runs never halt: a free-parameter invariant is likely.",
  "Risk: up to 16 phase types plus eating/overflow shapes."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "Record at 1,128,713 -> 127 = 2^7 - 1 counter steps -> next record at 1,173,120; checker C1-C7 pass.",
   "href": "proof.md"
  },
  {
   "kind": "fact",
   "text": "Phase rules: X1 -(16c+49)-> X0, X0 -(16c+49+6t)-> X1(g+1); Z1 -(8x+19)-> Z0, Z0 -(8x+43+6t)-> Z1(g+1), on random tapes.",
   "href": "scripts/check_proof.py"
  },
  {
   "kind": "fact",
   "text": "0 halts in 620 random-parameter runs of 1e8-2e8 steps (counter too long, too short, 5 record skeletons).",
   "href": "work/randparam_X0_seed7_300x2e8.txt"
  },
  {
   "kind": "fact",
   "text": "Shapes of 12 consecutive records: phases 1-4, eating of one digit per revolution.",
   "href": "work/inner_shapes_12rounds_from_1128713.txt"
  }
 ],
 "effort_if_yes": "One stage (about 2 h) to a closed shape set and a full case list in proof.md; formalization in further stages. The method carries to 528, 310 and 548 with their own words.",
 "updated": "2026-10-14",
 "answer": {
  "option": "fund_closure",
  "note": "",
  "date": "2026-10-14"
 }
}