{
 "tm": "1RB0LF_0RC0RB_1LC1LD_1RE0RD_---0RA_1LA0LF",
 "bucket_reason": "Priority call: deepen 2 marked #17 STUCK with no proof route in reach. The only route left is a multi-day project that needs your funding.",
 "question": "#17's cheap proof routes are closed: epoch induction is blocked on the tail, and no regular closed language exists at the sizes tried. Park it, or fund a multi-day particle-level simulator plus an invariant on particle sequences?",
 "options": [
  {
   "id": "park",
   "label": "Park #17 as STUCK",
   "consequence": "No compute. The exact left epoch map, the crossing and halting lemmas, the particle catalogue and the near-halt census to 4.31e13 are kept for a later Phase 3 attempt. targeting.md lists #17 as half of an exact twin pair, so that attempt would cover two machines."
  },
  {
   "id": "fund_particle",
   "label": "Fund the multi-day particle project",
   "consequence": "Build a particle-level accelerated simulator and a complete collision table, test the mod-4 right-end schedule out to epochs 11-12, then look for an invariant on particle sequences. Several days of agent time and open-ended; the catalogue was still growing at 363 types."
  },
  {
   "id": "far_probe",
   "label": "One more cheap probe: a larger-DFA FAR/CTL search",
   "consequence": "One ~2 h stage running a bounded decider with a bigger automaton than plain or parity CPS. The odds are low: the CPS counterexamples glue right-end 1-runs into the bulk, and the bulk's local language stopped saturating after E4."
  }
 ],
 "recommended": "park",
 "rationale": "The micro rules and the left recursion are exact: a_n = 171*3^n - 3 predicted epoch 5 before it was simulated. Halting reduces to one local pattern, and the machine has come near it only at the right edge (6 D1 events, all in E0 and E3, all reading 1). But the tail is a fossil-processing particle system whose catalogue keeps growing (363 types, with new ones in E7 and E8), and E8 rebuilt the right end without its 1^k run. Both cheap routes failed: plain CPS up to n = 20 and parity CPS up to n = 14 both give abstract HALT, and bulk saturation fails after E4. What remains is open-ended (several days) with no template, while four machines in this queue each need one well-defined lemma. Parking loses nothing, since the evidence is written up. With no halt to 4.31e13 and no near-halt ever seen in the bulk, it is not a promising halting candidate either.",
 "evidence": [
  {
   "kind": "rules",
   "text": "Epoch map P(a,c,T) -> P(3a+6, 3a+c+2, T') 34/34, including 4 swapped-in tails; burst cycle 420/420; slow-phase cycle 86/86. The closed form a_n = 171*3^n - 3 predicted epoch 5 before it was simulated.",
   "href": "notes.md"
  },
  {
   "kind": "rules",
   "text": "Crossing lemma checked on all 931,918 sweeps to 3.54e10. Halting lemma (the machine halts iff 1 0 0 <F 0 0 (0 0 | 1 0 0) occurs) matched 7,886/7,888 random halts after step 40; the 2 misses come from the random start.",
   "href": "deepen.json"
  },
  {
   "kind": "data",
   "text": "No halt to 3.3e11 by direct simulation (exactly 6 D1 near-halts, none after step 2.497e9), and none to 4.31e13 by Quick_Sim, cross-checked cell for cell. The E8 right-end rebuild was re-run at cell level with 0 D1.",
   "href": "scripts/deepen2_out/longrun_3.3e11.txt"
  },
  {
   "kind": "open",
   "text": "The tail is a particle system with a growing catalogue: 363 particle types over 29,643 left-edge visits, with new ones in E7 and E8. The right end is rewritten only in E0, E3, E4, E7 and E8, which fits epoch = 0 or 3 mod 4 (a hypothesis from 9 epochs).",
   "href": "scripts/deepen2_out/tailmap.txt"
  },
  {
   "kind": "probe",
   "text": "Invariants tried, all failed: plain n-gram CPS (abstract HALT for n = 2..12, 16, 18, 20), parity-aware CPS (n = 3..14), and the static forbidden factor 0011 (writes create it 744,280 times to 4e9).",
   "href": "deepen.json"
  },
  {
   "kind": "figure",
   "text": "Tail particles at each epoch start, placed by distance from the right end: grey = fossil suffix unchanged since the previous start, blue = rewritten.",
   "href": "img/deepen2_tail_fossils.svg"
  }
 ],
 "effort_if_yes": "About 10 minutes: confirm STUCK in status.json with 'parked by Dennis' and update STATUS.md. No compute.",
 "updated": "2026-10-10",
 "answer": {
  "option": "park",
  "note": "Dennis: go with all recommendations (2026-10-10)",
  "date": "2026-10-10"
 }
}