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 "distance": {
  "d": 16,
  "P": {
   "value": 16,
   "confidence": "upper_bound",
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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)=(4,10), lift P=34. Exponent array E (rows a=0..3, columns l=0..9): [[16, 7, 5, 24, 0, 30, 30, 15, 14, 12], [18, 9, 29, 33, 23, 0, 19, 2, 26, 18], [2, 17, 2, 2, 11, 33, 29, 30, 31, 30], [15, 27, 25, 1, 30, 26, 25, 26, 31, 1]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 1], [2, 9], [3, 5], [4, 7], [6, 8]], \"0,2\": [[0, 4], [1, 9], [2, 5], [3, 6], [7, 8]], \"0,3\": [[0, 9], [1, 6], [2, 7], [3, 8], [4, 5]], \"1,2\": [[0, 3], [1, 5], [2, 7], [4, 8], [6, 9]], \"1,3\": [[0, 6], [1, 3], [2, 5], [4, 9], [7, 8]], \"2,3\": [[0, 5], [1, 8], [2, 4], [3, 9], [6, 7]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 16 is the lightest Pauli logical found through 444 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[170,37,18]] at this lift, as an upper bound; this search did not reach 18, so the entry is 2 short of the published value.",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 135326,
   "ris_trials_per_side": 444000000,
   "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 1200 trials per template (Perlmutter job 59705376, 2026-10-12), then 144 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 300 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 16."
  }
 }
}