{
 "tm": "1RB0RA_1LC0LD_1LE1LD_0LB0RE_1RF1LB_---0RA",
 "bucket_reason": "Medium confidence after the funded close_chain stage: the chain case is closed, but it rests on one bound for words that start with 1 (L9), which holds on every run checked and is not proved, so proof.md waits.",
 "question": "Fund one more stage to prove L9 (PC < 2^(D+1) for words that start with 1) and then write proof.md, write proof.md now with L9 as an open lemma, or park?",
 "options": [
  {
   "id": "prove_l9",
   "label": "One stage: prove L9, then write proof.md",
   "consequence": "Plan: find, natively, an invariant that ties the f weight of the word after a flush to the epoch length N, check it on random instances, then prove it by hand. If it closes, every phi-eat is covered and proof.md follows at high confidence. Stop rule: if L9 does not close within the stage, write proof.md with L9 stated as the one open lemma."
  },
  {
   "id": "proof_md_now",
   "label": "Write proof.md now, with L9 stated as an open lemma",
   "consequence": "Gives you a reviewable Checkpoint B document sooner: rules, flush lemmas L1-L8 and the chain lemmas C0-C5. It cannot go to formalization until L9 is proved."
  },
  {
   "id": "park",
   "label": "Park",
   "consequence": "Everything is in notes.md, deepen.json and scripts/chain_check.py, so a later stage can resume without redoing work."
  }
 ],
 "recommended": "prove_l9",
 "rationale": [
  "Closed: the chain case (C0-C5). Exhaustive to 9 blocks: 758,058 states, 0 breaks outside L9.",
  "Open: L9, which last stage's L7 also needs. It holds on 1,000,000 epochs from blank (max PC/2^D = 1.5625).",
  "Real machine: 1,000/1,000 whole epochs match the abstract rules."
 ],
 "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": "1,000,000 epochs from blank: 0 violations of C1-C5, L9 or F <= N; 3 chains, each of length 2, the latest at epochs 350,330-350,331",
   "href": "data/chain_blank_1M.json"
  },
  {
   "kind": "fact",
   "text": "Exhaustive to 9 blocks: 2,985 S1->S2 and 3,512 S2->S2 epochs, all inside the invariant; the only breaks are L9, 7,880, all from small hand-made words",
   "href": "scripts/chain_exh.json"
  },
  {
   "kind": "fact",
   "text": "Real machine, one whole epoch from NM(phi U, 0, N): 1,000/1,000 match (553 S1, 372 S2, 75 other)",
   "href": "scripts/chain_tm.json"
  }
 ],
 "effort_if_yes": "One stage (about 2 h) for L9 and proof.md; then 2-3 stages to formalize (BECv7-style block-list carry relation).",
 "updated": "2026-10-10",
 "answer": {
  "option": "prove_l9",
  "note": "Dennis: go with recommendations (2026-10-11)",
  "date": "2026-10-11"
 }
}