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 "distance": {
  "d": 16,
  "P": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": {
    "X": [
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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=32. Exponent array E (rows a=0..3, columns l=0..9): [[21, 2, 17, 19, 11, 14, 1, 20, 23, 23], [10, 26, 0, 30, 25, 22, 24, 0, 16, 28], [29, 1, 3, 1, 17, 30, 21, 15, 25, 27], [11, 27, 31, 0, 2, 7, 29, 12, 8, 8]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 2], [1, 7], [3, 8], [4, 6], [5, 9]], \"0,2\": [[0, 3], [1, 5], [2, 8], [4, 7], [6, 9]], \"0,3\": [[0, 5], [1, 6], [2, 7], [3, 4], [8, 9]], \"1,2\": [[0, 8], [1, 4], [2, 3], [5, 6], [7, 9]], \"1,3\": [[0, 1], [2, 4], [3, 7], [5, 8], [6, 9]], \"2,3\": [[0, 4], [1, 7], [2, 9], [3, 5], [6, 8]]}. 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 482 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[160,35,17]] at this lift, as an upper bound; this search did not reach 17, so the entry is 1 short of the published value.",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 143999,
   "ris_trials_per_side": 482000000,
   "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 59705375, 2026-10-12), then 132 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 350 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 16."
  }
 }
}