{
 "tm": "1RB0RA_1LC0LF_1LE0LD_1LB---_1RA1LB_0LD0RC",
 "bucket_reason": "Med confidence after deepen: the mechanism is ruled exactly, but non-halting rests on one unproven size invariant.",
 "question": "Spend one stage proving R2's size invariant (every pending t clears before the next eat) and then write proof.md, or park R2 until #29's eat work gives a shared lemma?",
 "options": [
  {
   "id": "size_invariant",
   "label": "One stage (2 h): derive the size invariant, then proof.md",
   "consequence": "Search natively on the validated epoch model for an inductive invariant, for example pending-t height h <= #top-block digits - 2 together with N >= 2^(D-1). Check it on the model to N = 1e7 and on random states. If it closes, write proof.md (INC, EAT, shift, invariant) and plan a BECv7-style busycoq file. If no inductive form is found within the stage, report STUCK and say which arithmetic it would need."
  },
  {
   "id": "wait_29",
   "label": "Park until #29's eat is ruled",
   "consequence": "#29 has the same z/o/s/t alphabet and the same one-cell shift at its eat. If its stage yields a counter/shift lemma, R2's proof could reuse it. R2 waits at least one stage."
  },
  {
   "id": "park",
   "label": "Park as STUCK at deepen",
   "consequence": "No spend. The model and validation stay on file. The size invariant stays open."
  }
 ],
 "recommended": "size_invariant",
 "rationale": [
  "All regimes from blank follow exact validated rules (1,967,317 incs and 1,082/1,082 eats to 1e11).",
  "Only the size invariant is open; its observed margin is wide (t's clear in 1/4.6 of an epoch).",
  "The epoch model runs 1e5 epochs/s, so a native invariant search is cheap; #29's eat is not ruled yet."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "Epoch model reproduces all 1,079 epochs (Nold, e') from step 241 to 1e11 exactly",
   "href": "scripts/deepen/results/epochmodel_check_1e11.txt"
  },
  {
   "kind": "fact",
   "text": "Lockstep from blank to 1e11: INC 1,967,317/1,967,317; eats 1,082/1,082 (e', first-round parity, post-eat word)",
   "href": "scripts/deepen/results/lockstep_1e11.txt"
  },
  {
   "kind": "fact",
   "text": "Size bound needed: real states with N in [N/2, 2N] are safe 600/600; with N <= 10|W| some fail (t still present at the eat)",
   "href": "scripts/deepen/results/nfuzz_7.txt"
  },
  {
   "kind": "figure",
   "text": "Fig 2: rounds aligned at the bell boundary; each triangle is an epoch",
   "href": "card.html#fig-2"
  }
 ],
 "effort_if_yes": "One stage, at most 2 h, pure Python on the epoch model (one niced process). proof.md follows if the invariant closes. Coq is not used in this stage.",
 "updated": "2026-10-10",
 "answer": {
  "option": "size_invariant",
  "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"
 }
}