{
 "tm": "1RB0RF_1RC1RF_1LD1RA_---0LE_1LA0LE_0RA0LC",
 "bucket_reason": "Priority call: STUCK at informal_proof on a single open lemma, Lemma X (slack >= 0 after every excursion). The choice is more budget or a cryptid flag.",
 "question": "Fund one more stage on Lemma X (classify the excursion entries exactly), on the condition that if the entry types do not close into a finite list within the stage, #10 gets flagged CRYPTID_CANDIDATE?",
 "options": [
  {
   "id": "lemma_x",
   "label": "One more stage on Lemma X, with the cryptid flag as the exit",
   "consequence": "About 2 h of agent time. Classify the excursion entries (the cascade, and near-cascades such as 2^(B-1)+2^(B-2) and 2^(B-1)+2^(B-3)), follow each one exactly as cascade lemma (ii)-(iii) already does, and add the cases to check_proof.py. If it closes: proof.md revision 3, then Checkpoint B, then formalization, with the twin following as a delta. If not: CRYPTID_CANDIDATE, with proof.md sections 5.5-5.6 as the heuristic."
  },
  {
   "id": "cryptid_now",
   "label": "Flag CRYPTID_CANDIDATE now",
   "consequence": "Stop proof work and formalize only the rule layer, AntiHydra-style, at low priority. This gives up on the machine in this batch that is closest to a proof, at a point where every excursion examined has been safe by exact arithmetic, not by luck."
  },
  {
   "id": "park",
   "label": "Park as STUCK, without a flag",
   "consequence": "Costs nothing now. Lemma X stays open, with no date for returning to it."
  }
 ],
 "recommended": "lemma_x",
 "rationale": "Of the machines in this batch, #10 is the closest to a kill. The rule layer is exact and its L1 lemmas are written (check_proof.py revision 2: all checks pass). The epoch map has a closed form that reproduces 1,142 of 1,142 TM epochs to 1e11 steps. Proved lemmas (the cascade lemma, Lemma Z and Lemma R) reduce non-halting to one statement about the epochs after an excursion. The data favour a finite case analysis. Excursions are rare and short: at most 2 epochs on natural orbits and 4 in constructed ones. Of 1,087 excursion entries in check 7, 1,052 follow a cascade. In a separate scratch run, 125 of 127 did, and the other 2 followed a near-cascade of the kind the plan names. There are 0 violations in 6M eats on other orbits, in the skeptic's 2e9 eats, on the main orbit to 1e10 epochs and in 324,956 constructed cascade starts. Every case examined is excluded by exact arithmetic, which is not what a cryptid looks like. The honest risk is that the entry types do not form a small list. Magnitude bounds provably cannot prove Lemma X (the super-cascade shows this), and arbitrary starts do violate, which is why the stage has a hard exit to the cryptid flag. A success also covers the trajectory twin 1RB0RE_1RC1RE_1LD1RA_1LA0LD_0RA0LF_1LD---.",
 "evidence": [
  {
   "kind": "validation",
   "text": "check_proof.py revision 2: all checks pass (seed 2, 69 s). These include the exact L1 lemmas TG/CA/BL/FT/JW010/Eentry and the rule layer R/B/E at 1000/1000 each.",
   "href": "scripts/check_proof_full.log"
  },
  {
   "kind": "sim",
   "text": "The abstract epoch map equals the TM on 1,142 of 1,142 epochs to 1e11 steps (n goes from 2 to 8,416).",
   "href": "deepen.json"
  },
  {
   "kind": "analysis",
   "text": "Proved reduction: cascade lemma (i)-(iii), Lemma Z and Lemma R reduce Lemma N to Lemma X, which concerns excursions only.",
   "href": "proof.md"
  },
  {
   "kind": "sim",
   "text": "Main orbit: slack >= 0 at all 400,000 epochs checked. The minimum, 0, occurs only at t = 350,273, right after the cascade. The skeptic's run to 1e10 epochs adds no further slack-0 eats."
  },
  {
   "kind": "analysis",
   "text": "Other orbits: 0 non-normalized eats in 6M eats (2,000 x 3,000) and in the skeptic's 2e9. Of 1,087 excursion entries in check 7, 1,052 come right after a cascade. In a separate scratch run, 125 of 127 did, and the 2 others followed a near-cascade. 0 violations in 324,956 constructed cascade and near-cascade starts.",
   "href": "proof.md"
  },
  {
   "kind": "risk",
   "text": "Magnitude bounds cannot prove Lemma X: the super-cascade at n=1019 gives slack -1. Arbitrary starts also violate (two are confirmed on the TM). So the proof must describe the reachable residues exactly."
  },
  {
   "kind": "doc",
   "text": "Twin: 1RB0RE_1RC1RE_1LD1RA_1LA0LD_0RA0LF_1LD--- has the same trajectory (sheet row 1032, blank).",
   "href": "../../reports/targeting.md"
  }
 ],
 "effort_if_yes": "One stage: about 2 h of agent time, with at most 1 process for check_proof.py runs. If Lemma X closes: proof.md revision 3, then a formalization shaped like BECv7/FractalBEC, estimated at 15-30 KB of Rocq over 1-2 stages, plus a delta for the twin.",
 "updated": "2026-10-10",
 "answer": {
  "option": "lemma_x",
  "note": "Dennis: go with all recommendations (2026-10-10)",
  "date": "2026-10-10"
 }
}