{
 "tm": "1RB0RA_1LC0RE_0LC0LD_1RD1LB_0RF1RA_0RB---",
 "bucket_reason": "STUCK after two funded stages (pass 2 and the pass-3 review fix). The rest is new mathematics beyond the stage budget, so continuing needs Dennis's call.",
 "question": "Fund one more stage (at most 2 h) to prove Lemma T and find the shape condition K that closes twin #2's domain, or park it as STUCK?",
 "options": [
  {
   "id": "fund_k",
   "label": "One more stage on Lemma T and condition K",
   "consequence": "Try the potential-function proof of T (count times 2^position plus the V* of the rest) and search for K on L positions of the threshold output, testing closure from inside at large N. If both close, proof.md gets a complete argument and Rocq work starts (Lemmas A-D, U, B: several stages, since there is no template). If not, park with a sharper statement."
  },
  {
   "id": "park",
   "label": "Park as STUCK",
   "consequence": "Keeps the reduction (rules compiled, domain = one inequality, exact affine law V*(x') = N + c(x)) for a later attempt. It gives up a non-cryptid machine whose orbit is robust: no domain failure in 10,000 random steps."
  }
 ],
 "recommended": "park",
 "rationale": [
  "Rules, sweep and start compile; the domain is one inequality, and V* makes the sweep affine.",
  "Missing: a proof of Lemma T and a condition K on L positions. Both are new math, and so is the Rocq port.",
  "Park unless the queue runs dry: one kill for several stages of new work."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "J4 := ends with 1 and V* <= 2N+1 fails at (257, 10000000L1): V*(x') = 642 > 519, yet theta(x') = 94 <= N' (check 9i).",
   "href": "proof.md"
  },
  {
   "kind": "fact",
   "text": "400 random J4 starts x 25 sweeps: theta <= N at every step; V*/N falls below about 1.45 after two sweeps (check 9j).",
   "href": "check_proof.py"
  },
  {
   "kind": "fact",
   "text": "Without the new RIncs_eq, 75 of 15,593 G words have no derivation. With it all do, and Example sweep_LS01 compiles (5/5 closed).",
   "href": "scripts/TwinSpec.v"
  },
  {
   "kind": "link",
   "text": "proof.md section 3.3.5: the open problem stated precisely",
   "href": "proof.md"
  }
 ],
 "effort_if_yes": "One stage, at most 2 h, light compute (pure-Python closure tests, one niced process). Formalization afterwards: several stages.",
 "updated": "2026-10-10",
 "answer": {
  "option": "park",
  "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"
 }
}