{
 "tm": "1RB---_1LC1RE_1LD0LC_1LE1LC_1RF0RE_1RA0RB",
 "bucket_reason": "Medium confidence after deepen round 2 (recommend: more_observation). Proof work at medium confidence needs Dennis's call.",
 "question": "Spend one short targeted stage on rules for the shift-on-wall (0111000) states before proof.md, start proof.md now with the wrap coincidence as an open lemma, or park?",
 "options": [
  {
   "id": "targeted_deepen",
   "label": "One targeted stage (at most 2 h): rules for the shift-on-wall states",
   "consequence": "Run arr.py for 2-4 arrivals on 0111000 plus context, across wall types and wire lengths. If every case returns to L_gap, a closed superset L_gap+ is a purely structural invariant and proof.md can start: nursery period, interior-wire lemma, and closure under the unit rewrite. If some case does not return, only the timing argument is left, and Dennis gets a sharper call on whether that counts as pseudo-random arithmetic."
  },
  {
   "id": "proof_now",
   "label": "Start proof.md now, coincidence left open",
   "consequence": "proof.md would be conditional on one lemma, as #13's is, and a skeptic review would mark that gap fatal. Rules for the escape states would still be needed before Rocq."
  },
  {
   "id": "park",
   "label": "Park",
   "consequence": "Gives up a machine whose whole run is one exact rewrite (79,527/79,527 arrivals) with one narrow open point."
  }
 ],
 "recommended": "targeted_deepen",
 "rationale": "Everything right of the nursery is one cell language, L_gap, with 0 violations at 2,251 left records to 2e10. One B arrival is an exact unit carry rewrite, matching the machine on 79,527 of 79,527 random arrivals. The run can leave L_gap only through one counter-wrap coincidence, a shift landing on a wall. Forcing that coincidence 400 times gave 154 exits and 0 halts in 3,000 arrivals, so the exit states look harmless, but they have no rules yet. The next experiment is small and decisive. A few arrivals on 0111000, run in isolation, are exact, because the right end only receives B and returns C. The result decides between a structural invariant (proof can start) and a timing argument (back to Dennis). Starting proof.md first would only produce a conditional proof with a known fatal gap.",
 "evidence": [
  {
   "kind": "deepen",
   "text": "L_gap (runs of 1-3; gaps >= 3 and 0 or 3 mod 4; 3-runs only after a gap of 3 mod 4): 0 violations at 2,251 left records from 2e5 to 2e10 (realcheck.py).",
   "href": "scripts/deepen2/results/realcheck_2e10.txt"
  },
  {
   "kind": "rules",
   "text": "The unit carry rewrite equals the machine on 79,527/79,527 random arrivals (checkinc.py). 13 junction rewrites plus 6 sweep macros reproduce the blank run exactly to 20,000,003,117 steps.",
   "href": "deepen.json"
  },
  {
   "kind": "open",
   "text": "The only exit from L_gap: a W with a 1-block wire finishes a round while k >= 2 digits wrap from 2^k-3 to 0, and the next unit is a wall. Forced 400 times: 154 exits, 0 halts in 3,000 arrivals (coinc.py). A looser language with 4-runs halts once in 3,000 (explore5.py), so the exit states need exact rules.",
   "href": "notes.md"
  },
  {
   "kind": "data",
   "text": "Blank run: at most 1 zone wall at a time. 11 of 2,251 left records have one, none after 2e9, and 6 of those 11 sit on digits only (zonewalls2.py).",
   "href": "scripts/deepen2/results/zonewalls_2e10.json"
  },
  {
   "kind": "status",
   "text": "status.json: CHECKPOINT_A, stage deepen2, confidence med.",
   "href": "status.json"
  },
  {
   "kind": "figure",
   "text": "Card Fig 2: phase map. Colour bands are segments drifting right (the 3/2 conveyor).",
   "href": "card.html#fig-2"
  }
 ],
 "effort_if_yes": "One stage, at most 2 h of agent time, with light compute (arr.py runs the right end in isolation, one niced process). If L_gap+ closes, proof.md is the next stage, then a new-class formalization with no template (estimated 30-60 KB of .v, several stages).",
 "updated": "2026-10-10",
 "answer": {
  "option": "targeted_deepen",
  "note": "Dennis: go with all recommendations (2026-10-10)",
  "date": "2026-10-10"
 }
}