{
 "tm": "1RB0RF_1RC0RE_1LD1RA_1LA0LD_1RA---_0RA0LB",
 "bucket_reason": "Med confidence at observe: the rule table covers every hub from blank, but the non-halting argument has one unproved lemma; proof work waits.",
 "question": "Should R3 get a proof-prep stage on the cleanup lemma (x/z/w marks left by the bell vanish before the next b=0), done together with R2's size invariant, or be parked?",
 "options": [
  {
   "id": "prep",
   "label": "Proof-prep stage on the cleanup lemma (shared with R2)",
   "consequence": "Derive the carry transducer on sigma-words natively, prove the 2^(p+1) <= N bound on paper, fuzz it, then write proof.md and start the .v from FractalBEC.v + a digit-list counter."
  },
  {
   "id": "proof",
   "label": "Go straight to proof.md and Rocq, treating cleanup as the first lemma",
   "consequence": "Faster if the lemma is easy; risks a STUCK at the formal stage like the #10/#30 sibling."
  },
  {
   "id": "park",
   "label": "Park R3 behind the other Bell-eats-counter machines",
   "consequence": "No more agent time now; revisit after R2 or #29 produce a reusable shift/size lemma."
  }
 ],
 "recommended": "prep",
 "rationale": [
  "All hubs from blank to 1e9 and all b=0 hubs to 3e10 fit R1/E/B0/B1; the macro model never meets a mark at b=0.",
  "The gap is structural: marks come only from sigma of J blocks and clear within 2^floor(log2 N) increments.",
  "R2 needs the same 'marks clear before the next eat' lemma, so one stage can serve both."
 ],
 "evidence": [
  {
   "kind": "figure",
   "text": "Hub rows: gap and counter over four epochs",
   "href": "img/hubs_counter_epochs.png"
  },
  {
   "kind": "figure",
   "text": "Close-up: bounces, partial eat E, bell B1",
   "href": "img/explore_constructed_eat.png"
  },
  {
   "kind": "fact",
   "text": "Lockstep from blank: 192,529/192,529 hub transitions to 1e9; macro b=0 events match all 1,394 direct ones to 3e10.",
   "href": "notes.md"
  },
  {
   "kind": "fact",
   "text": "Arbitrary marked words halt (K(5,6,1z0101) halts in 19 steps), so the invariant must track where sigma puts marks.",
   "href": "scripts/l0test.py"
  }
 ],
 "effort_if_yes": "About 2 h of agent time for the lemma and proof.md; formalization after that is a separate stage.",
 "updated": "2026-10-10",
 "answer": {
  "option": "prep",
  "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"
 }
}