{
 "tm": "1RB0RA_1LC0LF_1LE0LD_1LB---_1RA1LB_0LD0RC",
 "bucket_reason": "STUCK at the size-invariant stage, confidence med: non-halting now rests on one inequality (R1: T_k + 1 <= I_k), but no inductive proof of it was found.",
 "question": "R2's size invariant is reduced to one inequality that needs a crossing lemma near powers of two: park R2 until #29/R3's size-invariant stages report, fund an R2 crossing-lemma stage now, or park it for good?",
 "options": [
  {
   "id": "wait_shared",
   "label": "Park until #29 / R3 report on the same lemma",
   "consequence": "No spend now. #29 and R3 are working on the same 'debris clears before the next eat' lemma right now. If either finds an inductive form, port it to R2 (its reduction to R1 is ready, and its epoch model runs 1e5 epochs/s), then write proof.md. Revisit R2 when both have reported."
  },
  {
   "id": "crossing",
   "label": "One stage (2 h): crossing lemma on R2",
   "consequence": "Model a passage of V* through 2^m natively: state = (delta mod 2^r, low part of the word, T). Test whether it is scale-invariant for m >= m0, so a finite crossing automaton bounds T/I. Cover m < m0 by the epoch model. If it closes, proof.md follows. If not, R2 stays STUCK with the automaton on file."
  },
  {
   "id": "park",
   "label": "Park as STUCK",
   "consequence": "No spend. The reduction (Lemmas A to E), the epoch model and all validation stay on file. R1 stays open."
  }
 ],
 "recommended": "wait_shared",
 "rationale": [
  "One inequality is open: R1 holds at all 808,539 epochs to N = 1e7 (T/I <= 0.13 for N >= 2^14).",
  "Size-only invariants are not inductive, so a crossing argument is needed.",
  "#29 and R3 face the same lemma now; waiting costs nothing."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "Gaps never grow (20.6M ball-eats to N = 1e7, 743k random); births outside one special case satisfy 2^h1 <= V*/2; R1 holds at every epoch",
   "href": "scripts/sizeinv/results/firstt_1e7.txt"
  },
  {
   "kind": "fact",
   "text": "R1 margin per octave of N to 1e7: T/I <= 0.28 (2^13 octave), <= 0.13 for N >= 2^14",
   "href": "scripts/sizeinv/results/binned_1e7.txt"
  },
  {
   "kind": "fact",
   "text": "Near-power-of-two random states break the size-only candidates Ja/Jb/Jc (44/601/668 of 2000 within 3 epochs)",
   "href": "scripts/sizeinv/results/randinv2_2.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": "wait_shared: none now, a short port stage later. crossing: one stage, at most 2 h, pure Python, one niced process, no Coq.",
 "updated": "2026-10-10",
 "answer": {
  "option": "wait_shared",
  "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"
 }
}