{
 "tm": "1RB0RA_1LC0LF_1LE0LD_1LB---_1RA1LB_0LB0RC",
 "bucket_reason": "Priority call: after the deepen stage the confidence is still med. The eat is ruled and safe, but one size invariant is open, so proof work waits for Dennis (CLAUDE.md).",
 "question": "With #29's eat ruled and safe for every t-free counter, fund one ~2 h stage on the last size invariant (eat-made t units clear before the next eat), or park #29 as STUCK at it?",
 "options": [
  {
   "id": "size_invariant",
   "label": "Fund one ~2 h stage on the size invariant",
   "consequence": "The agent writes a unit-level rule for the rounds whose carry enters a t segment (304 of 529 epochs have them), with an exact t-lifetime formula k0(P). It builds an epoch model (W, c) -> (W', c') and runs it far past 1e10 steps (R2 reached N = 1e7 this way), then looks for the inductive reason the margin holds. Exit: if a closed invariant is found, proof.md comes back to you at medium-high confidence. If the margin shrinks with N, or the shifted carry resists a rule within the stage, #29 is parked as STUCK with the rules kept."
  },
  {
   "id": "joint_r2",
   "label": "The same stage, run jointly with sibling R2",
   "consequence": "R2 (F0 = 0LD) reduced to the same lemma ('every t cleared before the next eat') and already has an epoch model to N = 1e7. One shared analysis could cover both machines. The two machines have different marker steps and eat sizes, so the epoch models stay separate. Expect about the same effort per machine, plus coordination."
  },
  {
   "id": "park",
   "label": "Park #29 as STUCK at the size invariant",
   "consequence": "No compute. Status becomes STUCK with the open lemma stated precisely. The sweep laws, the phase table, the eat law and the counter invariant stay in notes.md and deepen.json for a later family pass."
  }
 ],
 "recommended": "size_invariant",
 "rationale": [
  "Eat solved: every t-free word eats safely (to 12 units); value(W) = c+1 at all 529 eats.",
  "Left: one needed inequality (early eats halt 173/7,830), margin >= 3.5x (>= 8x at N >= 1000).",
  "An epoch model tests cheaply if the margin is structural; no cryptid (eat ignores the bits)."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "EAT law: all 354,293 t-free words up to 12 units reach a clean post-eat K-moment with no halt, and the result does not depend on c. Random 13-45-unit words: 1,500/1,500.",
   "href": "scripts/deepen/validate_deepen.json"
  },
  {
   "kind": "fact",
   "text": "Counter invariant on all 529 epochs to 1e10: value(W) = c+1 at each eat, and value(P) = 2 after it.",
   "href": "data/deepen/eat_episodes_1e10.txt"
  },
  {
   "kind": "fact",
   "text": "t-lifetime: (k0+1)/N <= 0.286 on every real epoch (<= 0.124 for N >= 1000), but forced early eats halt 173 times in 7,830.",
   "href": "data/deepen/epoch_tlifetime_1e10.txt"
  },
  {
   "kind": "fact",
   "text": "Closure fuzz: 0 halts in 400 x 3 + 3300 x 4 epochs from counter-consistent starts, power-of-two counters included. At the second eat, 5 starts still carry t units, so the invariant needs the reachable spacer structure.",
   "href": "notes.md"
  }
 ],
 "effort_if_yes": "One ~2 h stage with 1-2 light processes: a Python/C epoch model plus fuzz. No Rocq work. It returns either proof.md go/no-go or a STUCK park.",
 "updated": "2026-10-10",
 "answer": {
  "option": "size_invariant",
  "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"
 }
}