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  "P": {
   "value": 10,
   "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)=(4,12), lift P=20. Exponent array E (rows a=0..3, columns l=0..11): [[7, 0, 4, 2, 5, 19, 9, 7, 12, 3, 0, 11], [17, 6, 15, 11, 7, 8, 12, 6, 3, 0, 1, 19], [6, 16, 1, 6, 4, 5, 3, 17, 0, 18, 1, 12], [9, 19, 2, 8, 8, 4, 17, 5, 11, 14, 16, 12]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 4], [1, 3], [2, 6], [5, 9], [7, 10], [8, 11]], \"0,2\": [[0, 9], [1, 6], [2, 7], [3, 5], [4, 8], [10, 11]], \"0,3\": [[0, 8], [1, 4], [2, 10], [3, 7], [5, 11], [6, 9]], \"1,2\": [[0, 10], [1, 5], [2, 8], [3, 4], [6, 7], [9, 11]], \"1,3\": [[0, 5], [1, 11], [2, 7], [3, 10], [4, 9], [6, 8]], \"2,3\": [[0, 1], [2, 9], [3, 6], [4, 11], [5, 10], [7, 8]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 10 is the lightest Pauli logical found through 816 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[120,43,8]] at this lift, as an exact value; this template reads 10, above the table's value, and the two are different codes.",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 56412,
   "ris_trials_per_side": 816000000,
   "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 2000 trials per template (Perlmutter job 59705503, 2026-10-12), then 216 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 600 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 10."
  }
 }
}