{
 "tm": "1RB0RA_1LC0LD_1LE1LD_0LB0RE_1RF1LB_---0RA",
 "bucket_reason": "Medium confidence after the funded flush_proof stage: the flush lemma is proved except for one narrow arithmetic case (chains), so proof.md waits.",
 "question": "Fund one more stage to close the chain case and then write proof.md, write proof.md now with the chain case as a stated open lemma, or park?",
 "options": [
  {
   "id": "close_chain",
   "label": "One stage: prove the chain case (two phi-eats in a row whose word starts with f), then write proof.md",
   "consequence": "Uses the lemmas already proved (exact flush time F = 2^(1+D_F), budget v <= m). The plan is to show the chain's top run has length 1 and its carry stays <= 1. If that closes, proof.md follows at high confidence. Stop rule: if it does not close within the stage, write proof.md with the case flagged."
  },
  {
   "id": "proof_md_now",
   "label": "Write proof.md now, with the chain case stated as an open lemma",
   "consequence": "Gives you a reviewable Checkpoint B document sooner. It cannot go to formalization until the open lemma is proved."
  },
  {
   "id": "park",
   "label": "Park",
   "consequence": "Everything is in notes.md, deepen.json and scripts/flush_check.py, so a later stage can resume without redoing work."
  }
 ],
 "recommended": "close_chain",
 "rationale": [
  "Proved: F = 2^(1+D_F); F <= N if the word starts with 1, at EAT0z, and in bottom-exact cases.",
  "Open: chains. 200,000 epochs from blank: 0 violations, worst F/N 0.505, bad sub-case never.",
  "Random checks: 19,236/19,236 abstract and 256/256 real-machine flushes match the formula."
 ],
 "evidence": [
  {
   "kind": "figure",
   "text": "Fig 2: one row per left entry into E; the diagonal 00 marker runs down to the counter band, then an eat",
   "href": "card.html#fig-2"
  },
  {
   "kind": "fact",
   "text": "1e10 run, 567 epochs: 1,004,198 rounds identical to the TM dump; lemmas L1-L5 hold at every round",
   "href": "scripts/flush_check.py"
  },
  {
   "kind": "fact",
   "text": "200,000-epoch abstract run: 0 violations, worst F/N 0.505, chains at epochs 1115-1116 and 2061-2062",
   "href": "data/flush_fast_200k.json"
  },
  {
   "kind": "fact",
   "text": "Random U: L1/L2/L3 19,236/19,236 (abstract), flush time on the real machine 256/256",
   "href": "scripts/flush_random.json"
  }
 ],
 "effort_if_yes": "One stage (about 2 h) for the chain case and proof.md; then 2-3 stages to formalize (BECv7-style block-list carry relation).",
 "updated": "2026-10-10",
 "answer": {
  "option": "close_chain",
  "note": "auto-applied: Claude's recommendation, under Dennis's standing instruction 'do your recommendations and continuously orchestrate' (2026-10-10, while he was away). Override any time.",
  "date": "2026-10-10"
 }
}