{
 "tm": "1RB0RA_1LC0LF_1LE0LD_1LB---_1RA1LB_0LB0RC",
 "bucket_reason": "Priority call: after the size-invariant stage the confidence is still med. Every round is ruled and the epoch model is clean to N = 1e8, but the size bound is exactly tight and, in rare leading-spacer epochs, depends on the counter's low bits, so proof work waits for Dennis (CLAUDE.md).",
 "question": "With every #29 round ruled and the size bound proven by test except in rare leading-spacer epochs (where a surviving t has always recovered), fund one ~2 h recovery stage, or park #29 as STUCK?",
 "options": [
  {
   "id": "recovery",
   "label": "Fund one ~2 h recovery stage",
   "consequence": "The agent writes the informal proof of the generic lemma (h(eat(W)) <= D(W)-1 when the eat word starts with a digit) from the CASCADE rule and the eat recursion. For the leading-spacer case it proves a recovery lemma instead of the bound: a top t that survives one eat is cleared in the next epoch without halting. This needs one more rule, for the transient v = 110 unit. It is checked by layout over all bit patterns. Exit: proof.md comes back to you at medium-high confidence; if the recovery itself depends on the counter's bits, #29 is flagged CRYPTID_CANDIDATE; otherwise STUCK."
  },
  {
   "id": "park",
   "label": "Park #29 as STUCK at the leading-spacer case",
   "consequence": "No compute. Status becomes STUCK with the open lemma stated precisely: the generic lemma (true by exhaustive test) and the leading-spacer recovery. The CASCADE rule, the exact t-lifetime law, the epoch model and all tests stay in notes.md and deepen.json for a later family pass with R2."
  }
 ],
 "recommended": "recovery",
 "rationale": [
  "All rounds ruled (CASCADE, 10,371/10,371 real rounds); epoch model clean from blank to N = 1e8.",
  "Generic size lemma holds for every t-free word to 12 units; leading-spacer eats are rare (6 to 1e7).",
  "There a surviving top t always recovered within 2 epochs, 0 halts in 24,576 patterns."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "Epoch model from blank to N = 1e8 (~7.1M epochs): 0 halts, 0 t at any eat; k0 + 2 = 2^h in all 7,015,292 epochs with t.",
   "href": "data/sizeinv/emodel_1e8_summary.txt"
  },
  {
   "kind": "fact",
   "text": "CASCADE rule (the shifted carry as one unit rule): 3,821/3,821 random words and 10,371/10,371 real exact rounds match the TM.",
   "href": "scripts/sizeinv/cascade_validate.json"
  },
  {
   "kind": "fact",
   "text": "Tight bound: the slack is 0 at N = 8,110, 16,221 and 4,193,610 (k0/N = 0.505). The deepen stage's >= 3.5x margin does not hold structurally.",
   "href": "notes.md"
  },
  {
   "kind": "fact",
   "text": "Leading-spacer layouts: one bit pattern per layout breaks the bound. In every test the machine recovers within 2 epochs with 0 halts (all 24,576 patterns on the real layouts with D <= 14).",
   "href": "scripts/sizeinv/leadhalt_real.json"
  }
 ],
 "effort_if_yes": "One ~2 h stage with 1-2 light processes (the existing Python/C tools), no Rocq. It returns proof.md at medium-high confidence, a CRYPTID_CANDIDATE flag, or a STUCK park.",
 "updated": "2026-10-10",
 "answer": {
  "option": "recovery",
  "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"
 }
}