{
 "tm": "1RB---_1LC1RE_1LD0LC_1LE1LC_1RF0RE_1RA0RB",
 "bucket_reason": "Medium confidence after the funded law stage. The interval law broke at nu2 = 7 (its irregular window grew from 7 to 15 residues), and the zone lemma needs the exact intervals, so proof work at medium confidence needs Dennis's call.",
 "question": "Spend one more stage deriving the intervals from the closed conveyor-top + zone system and proving the zone lemma by induction over 32-blocks, start proof.md now with both open, or park?",
 "options": [
  {
   "id": "top_system",
   "label": "One stage (at most 2 h): derive N from the closed top system, then the zone lemma by block induction",
   "consequence": "Model the last frozen level, the growing top wire and the zone as one system fed by its constant per-interval input. Show that its 32-block map takes the zone counter b+1 to b+2 symbolically, with the nu2(b+2) class as the case split, and get the window length for each nu2. Stop rule: if the window keeps growing with nu2 and no closed form appears, park."
  },
  {
   "id": "proof_md",
   "label": "Start proof.md now, with the interval law and the zone lemma as open lemmas",
   "consequence": "proof.md is written from the validated rules (nursery, carry rewrite, zone automaton, block counter). Both lemmas are marked open, and a skeptic would mark them fatal."
  },
  {
   "id": "park",
   "label": "Park",
   "consequence": "Keeps the 1.93e11 replay, the zone automaton, the block-counter finding and the synthetic tests on file, and stops work on this machine."
  }
 ],
 "recommended": "top_system",
 "rationale": [
  "Mechanism found: the zone holds b+1 in binary and the ruler tuples are its carry chains.",
  "N as an external table broke at nu2 = 7; random 15-residue windows give survivors (2/100).",
  "Real run: 0 zone walls alive at 4,820 absorptions; synthetic law runs to j = 3e5: 0."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "Replay to 1.93e11: 1,812/1,812 record intervals exact, 4,820 absorptions, 0 alive, 0 hits; nu2 = 7 tuple new; table fails at j = 4065..4072.",
   "href": "scripts/deepen5/results/nstruct_final.json"
  },
  {
   "kind": "fact",
   "text": "Zone digits above position 6 = b+1 at residues 0..17 (68/68 blocks); low part one form per residue for r = 1..18, all zero at r = 18.",
   "href": "scripts/deepen5/zcount.py"
  },
  {
   "kind": "fact",
   "text": "Zone lemma: 300/300 runs safe with random 7-residue windows; random 15-residue windows give a survivor in 2/100 runs.",
   "href": "scripts/deepen5/results/summary.json"
  },
  {
   "kind": "fact",
   "text": "Conveyor top: next last wire = w + L/3 with fixed point w = 2L/3, so N ~ 3L; the per-interval input to the top is constant within a level.",
   "href": "scripts/deepen5/toptrace.py"
  }
 ],
 "effort_if_yes": "One stage, at most 2 h of agent time, light compute (Python unit model and zone automaton; a longer replay toward the nu2 = 8 block at about 8.7e11 would be about 75 min of single-core C-core time in the background). If the block map closes, proof.md is next, then a new-class formalization with no template.",
 "updated": "2026-10-10",
 "answer": {
  "option": "top_system",
  "note": "Dennis: go with recommendations (2026-10-11)",
  "date": "2026-10-11"
 }
}