{
 "tm": "1RB0RE_1LC0RD_1LD0LD_1RA0LC_1RA1RF_1RA---",
 "bucket_reason": "Priority call: observe is done at LOW confidence. R4 is pool #32's table with the D start, and both machines are stuck on the same hierarchical-counter structure.",
 "question": "R4 and #32 are one table with one open mechanism: a hierarchical counter whose fossil-K walls lose one unit of fuel per lower overflow. Invest in a joint #32/R4 recursive invariant, or park both?",
 "options": [
  {
   "id": "park_both",
   "label": "Park R4 and #32 together for now",
   "consequence": "No compute. Both go to STUCK with a shared note: level 1 is kill #11's counter (M and O exact), plus P, the fuel law and the 3 unruled event types. A later joint stage would start from R4's and #32's scripts, and the compute moves to the medium-confidence machines."
  },
  {
   "id": "joint_rules_stage",
   "label": "Fund one joint ~2 h stage on the 3 unruled event types",
   "consequence": "Rule the far-end resets, the wall's v = 1 shape and the Z3-junction carries (54 of 12,438 macro steps to 3e8) in both orientations at once. Turn the fuel decrement and wall birth into exact rules, and run constructed small-fuel starts. This yields one exact abstract model covering both machines, but no invariant yet; expect 2-3 more stages before proof.md, if a proof exists at all."
  },
  {
   "id": "invariant_now",
   "label": "Go straight for a recursive multi-level invariant",
   "consequence": "Open-ended: several stages, possibly several days. Skipping the event rules means the invariant would rest on the 54 unruled steps."
  }
 ],
 "recommended": "park_both",
 "rationale": "The level-1 counter is solved territory: kill #11 and its mirror #33 share M and O verbatim. The part that decides halting is new. Walls form, burn fuel at one unit per lower overflow, dissolve and re-form, and the long run is out of reach: the inner wall's fuel is 151 at 2e10, which means about 150 more resets at growing intervals. Nothing is cryptid-like (resets come at b = 2^k - 3, fuel drops by exactly 1 per overflow, and two fuel-cut runs were benign to 2e8). So this is a deep structural proof, but it needs a multi-level invariant with no template, and 3 local event types must be ruled first. Together with #17 it is the furthest from proof.md in this queue. Parking both keeps one development for both machines when work resumes, and it frees compute for #37, #8, #18 and #29, which each need one well-defined lemma. If you want a Skelet-1-class push, the joint rules stage is the cheap way in.",
 "evidence": [
  {
   "kind": "rules",
   "text": "M_k (#33's carry) 300/300 random and 12,350/12,350 on the real run to 3e8. P (partial overflow) 300/300 plus 34/34 real. O 200/200; the negative control with one u = 1 digit passes 0/200.",
   "href": "notes.md"
  },
  {
   "kind": "data",
   "text": "Coverage to 3e8: 12,438 K-to-K steps, of which M 12,350, P 34, O 0 and other 54 (far-end terminators, the wall's v = 1 shape, Z3 junctions). These are the same three event types #32 left open.",
   "href": "scripts/classify_3e8.txt"
  },
  {
   "kind": "data",
   "text": "Fuel law, real run only: each reset that ends at the inner wall lowers its gap by exactly 1 (217 at 1.8e7; 179 at 2.84e8, over 38/38 resets; 151 at 2e10). Not checked on random instances.",
   "href": "scripts/resets_3e8.json"
  },
  {
   "kind": "probe",
   "text": "Fuel-cut runs (inner gap cut from 217 to 9 and to 5): the wall dissolves within about 3e4 steps, new walls form with fresh fuel (109, 164), and nothing halts to 2e8.",
   "href": "scripts/wall_cut104_run.jsonl"
  },
  {
   "kind": "data",
   "text": "Sparse run to 2e10: no halt. lo = -398,788; hi is 85, then 88 after about 1.4e10 (the level-2 overflow).",
   "href": "scripts/sparse_2e10.txt"
  },
  {
   "kind": "figure",
   "text": "Whole tape to 3e7: after the pinch near step 1.8e7, the right part keeps fixed bands while new bands grow from the left edge.",
   "href": "img/phase_full_3e7.png"
  },
  {
   "kind": "sibling",
   "text": "Pool #32 (same table, A start) is OPEN at stage rules, with the same three unruled event types (54 of 67,856 transitions to 1e10) and no proof.md.",
   "href": "../1RB0LC_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---/notes.md"
  }
 ],
 "effort_if_yes": "About 10 minutes: set both status.json files to STUCK with the shared note and update STATUS.md. No compute.",
 "updated": "2026-10-10",
 "answer": {
  "option": "park_both",
  "note": "Dennis: go with all recommendations (2026-10-10)",
  "date": "2026-10-10"
 }
}