{
 "tm": "1RB0LC_1RC0RA_1RD0RF_0LE---_1LB1LA_1LD1RA",
 "bucket_reason": "Mechanism confidence is still med after the funded parity stage. That stage answered the parity question, but closing the invariant also needs magnitude facts, so proof work waits for you.",
 "question": "Fund one stage to close #16's macro-level invariant (the parity rules plus the underflow inequality and the exact staircase relation), checked on random instances, before proof.md?",
 "options": [
  {
   "id": "macro_closure",
   "label": "One stage: close the macro-level invariant",
   "consequence": "About 2 h and 1-2 light processes, no Coq. Extend G1-G5 with three facts: P < d for a P-mode bouncer with walls, d >= 4 at every Push, and the ak + d staircase relation that makes every right end clean or top. Then rerun scripts/good_closure.py until no random instance leaves the predicate or halts. Exits: if it closes, write proof.md as a FractalType7v4-style Good predicate; if a leak can only be fixed with non-linear arithmetic, flag the machine cryptid-like."
  },
  {
   "id": "flag_cryptid",
   "label": "Flag cryptid-like, as the funded stop rule says",
   "consequence": "Status becomes CRYPTID_CANDIDATE. The stop rule fires on its wording, because G4 uses the mod-2 running sum ak + ΣB. But halting did not depend on magnitudes in any same-parity perturbation (0 halts in 264 runs), so this label is probably wrong."
  },
  {
   "id": "park",
   "label": "Park",
   "consequence": "Status becomes parked at parity_round. The new closed forms (EatChunk, RightEnd and the four right-phase rules) stay in notes.md. #39 and R7, which share #16's Quick_Sim signature, lose their lead."
  }
 ],
 "recommended": "macro_closure",
 "rationale": [
  "Halting has one local cause: eat-through of an odd (10)-run (all 95 random halts).",
  "Parities decide: same-parity perturbations never halt. The right phase is now in closed form.",
  "Left: closure. G1-G5 leak only through magnitude facts that hold from blank, not parity."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "Halting mechanism: eat-through of an odd (10)-run. 95/95 stress-test halts are of this kind; direct test 40/40 halt vs 0/40 with all runs even.",
   "href": "scripts/halt_classify.py"
  },
  {
   "kind": "fact",
   "text": "Parities decide: same-parity perturbations of reachable frames gave 0 halts (m2 0/80, r2 0/80, r2all 0/80, late frames 0/24); flipping one random exponent halts 2/40.",
   "href": "scripts/pt_r2_43.txt"
  },
  {
   "kind": "fact",
   "text": "G1-G5 hold at all 454 judged frames to 1.02e12. On 120 random G1-G5 frames, 73 leave the predicate and 2 halt, through P-mode right ends with walls and Push with d < 4; neither occurs from blank.",
   "href": "scripts/good_closure_82_good.txt"
  },
  {
   "kind": "fact",
   "text": "Parity-aware run-length DFA (no truncation, mod 2): abstract HALT after 1.1e5-2.1e5 configs, through tapes with many odd walls that never occur. With mod 4 it caps at 3e6.",
   "href": "scripts/ctl_parity_rl.txt"
  }
 ],
 "effort_if_yes": "One stage: about 2 h of agent time and 1-2 light processes (random-instance closure tests on the accelerated simulator). No Coq.",
 "updated": "2026-10-10",
 "answer": {
  "option": "macro_closure",
  "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"
 }
}