{
 "tm": "1RB0LC_1RC0RA_1RD0RF_0LE---_1LB1LA_1LD1RA",
 "bucket_reason": "Mechanism confidence is still med after the funded macro_closure stage. The decided closure test failed, and the invariant that would close it is not written down yet.",
 "question": "Fund one stage to write #16's hub-level invariant out explicitly (parity, staircase, linear underflow relations, corner-event rules) and test its closure with the macro simulator, before proof.md?",
 "options": [
  {
   "id": "hub_invariant",
   "label": "One stage: write the hub invariant out",
   "consequence": "About 2 h and 1-2 light processes, no Coq. Read the exact relations off hubs reached from blank (e.g. arrival d = q or q-1 after a merge-back). State H as parity + staircase + linear underflow inequalities. Rule or exclude the small-value corner events and EatToWall. Test closure over one traversal on random H-hubs with the macro simulator (target: 0 leaks in 10^4 hubs), then confirm on the accelerated simulator. Exits: closed -> proof.md (hub-to-hub induction, macro rules as lemmas); still leaking -> park."
  },
  {
   "id": "siblings",
   "label": "Check #39 and R7 first",
   "consequence": "About 1 h. Map #39 and R7 onto the same macro events (Push, Absorb, staircase). If one has a simpler wall structure, move the invariant work there. #16 waits."
  },
  {
   "id": "park",
   "label": "Park",
   "consequence": "Status becomes parked at macro_closure. The macro simulator, the 4 new rules and the closure data stay in notes.md and scripts/. #39 and R7 lose their lead."
  }
 ],
 "recommended": "hub_invariant",
 "rationale": [
  "From blank, validated rules cover 260,000 macro events (runs > 10^4300 cells) with no gap.",
  "Closure fails only through linear facts (underflow between walls) and small-value corner events.",
  "0 halts in every closure test, and no pseudo-random arithmetic, so it is not cryptid-like."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "The macro simulator matches the census from blank on 278/278 frames to 1.02e12. It then runs 260,000 events with no unruled situation.",
   "href": "scripts/macro_sim.py"
  },
  {
   "kind": "fact",
   "text": "The decided predicate is not closed: 54/80 random instances leave it within 3e7 steps (D=1), 22/80 with a 3-cycle lookahead; 0 halts.",
   "href": "scripts/good_closure2_151_D1.txt"
  },
  {
   "kind": "fact",
   "text": "Random hubs: 1,719/2,000 stay ruled for 40 right ends. Almost all failures are underflow at depth 2-3 (P-mode right end with walls).",
   "href": "scripts/hub_random_4_S_D40.txt"
  },
  {
   "kind": "fact",
   "text": "From blank, after a merge-back the outer bouncer reaches the next wall with d = q or q-1 (567/570), and Absorb happens only at the last wall.",
   "href": "scripts/push_relations_40k.txt"
  }
 ],
 "effort_if_yes": "One stage: about 2 h of agent time and 1-2 light processes (macro simulator, accelerated simulator). No Coq.",
 "updated": "2026-10-10",
 "answer": {
  "option": "hub_invariant",
  "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"
 }
}