{
 "tm": "1RB0RE_1LC0RD_1LD0LD_1RA0LC_1RA1RF_1RA---",
 "bucket_reason": "Priority call: the Class 2 close-out track for R4 and #32 (one table) ended in a cryptid flag after its third and last stage. Whether either machine halts turns on modular arithmetic at a hierarchy of fuel exhaustions.",
 "question": "R4 and #32 are flagged CRYPTID_CANDIDATE (halting decided by fuel residues at nested exhaustions, no invariant): stop here, or fund a recursive abstract model to follow R4's real orbit, whose top already has the halting residue?",
 "options": [
  {
   "id": "stop_cryptid",
   "label": "Stop: keep both as cryptid candidates",
   "consequence": "No more compute. Both stay CRYPTID_CANDIDATE with the rules written up (rule G in #32's proof.md, the regime maps and the cut tables in its notes.md). The class close-out lists them as cryptid candidates, not as kills."
  },
  {
   "id": "recursive_model",
   "label": "Fund a recursive abstract model (open-ended, several stages)",
   "consequence": "Derive each deep level's cycle map exactly (deep levels are not copies of the top: R4's deep wall loses 1 fuel per 2 kicks, the top loses 5 per 16), then simulate level by level in closed form to R4's next top exhaustion. It could show that R4 halts, at a step count far beyond 1e80 and probably only expressible symbolically. A non-halting proof is not in sight on this route."
  },
  {
   "id": "formalize_rules",
   "label": "Formalize the rule reduction only",
   "consequence": "Rocq lemmas for the token machine and rule G (as AntiHydra.v does for its rule), as a record of the reduction. No change to the open question; about 1-2 stages."
  }
 ],
 "recommended": "stop_cryptid",
 "rationale": [
  "The top halts iff its fuel runs out at N = 2 (mod 5): of N = 0..44, only 2, 7, 12, 17, 22 halt by 1e80.",
  "A lower digit that runs out first flips that irregularly (N = 12: 14 of 24 small u1 halt; N = 11: 0 of 25).",
  "Both orbits are frozen behind deep levels to 1e80; no invariant can ignore residues at every level."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "Wide-integer simulator (c2s3_tsim.c): reproduces stage 2 byte for byte to 1e37 and every earlier halting step count; no halt for either orbit to 1e80 steps.",
   "href": "machines/1RB0LC_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---/scripts/c2s3_tsim.c"
  },
  {
   "kind": "fact",
   "text": "u1 sweep from I(N, 360): N = 17 halts for u1 in {4, 7, 10, 13, 16, 21, 22} and 25..49, not for the other 18 values below 25. When u1 runs out in the first cycle, u1 = 1 (mod 3) tends to halt, with exceptions.",
   "href": "machines/1RB0LC_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---/notes.md"
  },
  {
   "kind": "fact",
   "text": "Heuristic: under a random-residue model each top-level regime-I exhaustion halts with probability about 1/5 or less, and the top keeps cycling, so the random model leans to an astronomically late halt, not to non-halting.",
   "href": "machines/1RB0LC_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---/notes.md"
  }
 ],
 "effort_if_yes": "recursive_model: open-ended, at least 3 stages of about 2 h each, with no guarantee of a result. formalize_rules: 1-2 stages.",
 "updated": "2026-10-12",
 "answer": {
  "option": "stop_cryptid",
  "note": "Dennis 2026-10-12: 'go with recommendations'",
  "date": "2026-10-12"
 }
}