{
 "tm": "1RB0LF_1RC1RB_0RD0RC_1LE1LF_1LD---_0LB1LA",
 "bucket_reason": "Priority call: deepen is done at medium confidence. K is closed and the sync is derived for the steady class, but one lemma about the bottom run is open, so proof work waits for Dennis.",
 "question": "#37's sync now rests on one open lemma B (its bottom counter run never again becomes an erasable 11 digit): fund a second deepen round on B, or park #37?",
 "options": [
  {
   "id": "deepen2",
   "label": "Fund a second ~2 h deepen round on lemma B",
   "consequence": "The agent tracks the bottom run and the gap above it at every carry of level >= 2 from the phase-11 start (step 150,742,757) and writes the finer grammar of the high digits that B needs (long runs that drift, gaps that shrink and merge). It checks that grammar for closure on random members. Exit: if B follows, proof.md is next (a visit-level proof from the phase-11 configuration). If B depends on the counter value in a way no regular grammar captures, the machine goes to STUCK."
  },
  {
   "id": "park",
   "label": "Park #37 behind the other machines",
   "consequence": "No compute. K, the exact block rule, the sync invariant, the low-end lemma and the steady-class induction are kept in notes.md and deepen.json."
  },
  {
   "id": "proof_now",
   "label": "Waive the med rule and start proof.md with B as a stated assumption",
   "consequence": "Everything except B is validated, so the write-up is mostly mechanical. A skeptic review would still send it back, because B is exactly where off-sync could enter (with a bottom 11 digit, 63 of 150 random runs go off-sync)."
  }
 ],
 "recommended": "deepen2",
 "rationale": [
  "All else is exact: K closure 18,000/18,000, block rule and sync 57,433/57,433.",
  "Since phase 11 the run is in a steady class closed by mod-8 arithmetic; only a short bottom run leaves it.",
  "B is structural (no arithmetic, no cryptid), so one round can plausibly settle it."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "Real run to 1.2e10: K 57,448/57,448, block rule 57,433/57,433, m mod 4 in {1,2} 57,433/57,433, low-end lemma 28,698/28,698, n' = 4 visits + 2 in 13/13 phases.",
   "href": "work/deepen/realcheck_1.2e10.txt"
  },
  {
   "kind": "fact",
   "text": "Forced resets on real words: a final gap >= 4 at the reset always gives a synced next phase (532/532); a gap of 3 depends on the bottom run.",
   "href": "work/deepen/forcereset_seed1.log"
  },
  {
   "kind": "fact",
   "text": "Steady class with a bottom run >= 3: 249/250 random runs stay in sync over 5 phases. With a bottom 11 digit: 63/150 go off-sync.",
   "href": "work/deepen/steady_seed3_rmin3.log"
  },
  {
   "kind": "fact",
   "text": "Since phase 11: n+2 = 1681 x 2^j, final gap 3 at every phase start and 4 at every reset, bottom run 26..80 cells.",
   "href": "notes.md"
  }
 ],
 "effort_if_yes": "One ~2 h deepen round with 1-2 light processes (C tracker scripts/deepen/lowend.c, Python checks); no Rocq. Next decision: proof.md go/no-go.",
 "updated": "2026-10-10",
 "answer": {
  "option": "deepen2",
  "note": "auto-applied: Claude's recommendation, under Dennis's standing instruction 'do your recommendations and continuously orchestrate' (2026-10-10, while he was at lunch). Override any time.",
  "date": "2026-10-10"
 }
}