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 },
 "distance": {
  "d": 12,
  "P": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": {
    "X": [
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     22,
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 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "origin": "submission",
  "construction": "search",
  "date": "2026-10-15",
  "references": [
   "arXiv:2609.30069"
  ],
  "notes": "Halved CPM pair-partition code of arXiv:2609.30069 (Definition 1, reversing fold of Proposition 4) at (J,L)=(4,12), lift P=28. Exponent array E (rows a=0..3, columns l=0..11): [[6, 12, 26, 18, 7, 5, 17, 18, 8, 20, 2, 9], [18, 27, 25, 17, 24, 22, 0, 24, 21, 10, 21, 3], [4, 13, 8, 7, 0, 9, 1, 20, 22, 1, 17, 12], [3, 5, 13, 8, 7, 24, 24, 23, 19, 7, 25, 12]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 10], [1, 11], [2, 3], [4, 5], [6, 9], [7, 8]], \"0,2\": [[0, 7], [1, 4], [2, 5], [3, 11], [6, 8], [9, 10]], \"0,3\": [[0, 9], [1, 8], [2, 11], [3, 4], [5, 6], [7, 10]], \"1,2\": [[0, 1], [2, 9], [3, 7], [4, 10], [5, 8], [6, 11]], \"1,3\": [[0, 6], [1, 3], [2, 10], [4, 7], [5, 9], [8, 11]], \"2,3\": [[0, 11], [1, 2], [3, 9], [4, 6], [5, 7], [8, 10]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 12 is the lightest Pauli logical found through 370 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[168,59,13]] at this lift, as an exact value; this search did not reach 13, so the entry is 1 short of the published value.",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 29903,
   "ris_trials_per_side": 370000000,
   "tool": "halved_pp.py templates; verify/heuristic_distance.py Pauli RIS; gf2_fast on the symplectic doubling under random per-qubit symplectic frames (frame_screen.py)",
   "notes": "Pauli-weight RIS screen at 1500 trials per template (Perlmutter job 59705503, 2026-10-12), then 120 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 250 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 12."
  }
 }
}