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  ]
 },
 "distance": {
  "d": 14,
  "P": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     2,
     16,
     37,
     50,
     59,
     60,
     81,
     97,
     114
    ],
    "Z": [
     2,
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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=30. Exponent array E (rows a=0..3, columns l=0..9): [[24, 20, 19, 3, 22, 26, 24, 4, 12, 3], [16, 26, 8, 17, 24, 19, 21, 9, 0, 13], [8, 28, 25, 24, 13, 10, 5, 19, 29, 10], [19, 3, 1, 21, 8, 5, 6, 6, 6, 18]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 5], [1, 2], [3, 4], [6, 9], [7, 8]], \"0,2\": [[0, 8], [1, 3], [2, 6], [4, 9], [5, 7]], \"0,3\": [[0, 4], [1, 9], [2, 7], [3, 5], [6, 8]], \"1,2\": [[0, 7], [1, 4], [2, 5], [3, 9], [6, 8]], \"1,3\": [[0, 9], [1, 7], [2, 4], [3, 8], [5, 6]], \"2,3\": [[0, 6], [1, 8], [2, 9], [3, 7], [4, 5]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 14 is the lightest Pauli logical found through 568 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[150,33,16]] at this lift, as an upper bound; this search did not reach 16, so the entry is 2 short of the published value.",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 268440,
   "ris_trials_per_side": 568000000,
   "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 168 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 400 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 14."
  }
 }
}