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    "X": [
     31,
     66,
     96,
     158
    ],
    "Z": [
     21,
     61,
     108,
     125
    ]
   }
  ]
 },
 "distance": {
  "d": 10,
  "P": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     4,
     6,
     19,
     48,
     137,
     150
    ],
    "Z": [
     4,
     6,
     19,
     41,
     43,
     88,
     98,
     150
    ]
   }
  }
 },
 "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)=(3,8), lift P=40. Exponent array E (rows a=0..2, columns l=0..7): [[38, 8, 36, 5, 21, 21, 0, 7], [17, 38, 20, 2, 28, 17, 2, 36], [8, 20, 13, 20, 23, 27, 1, 4]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 6], [1, 3], [2, 4], [5, 7]], \"0,2\": [[0, 3], [1, 2], [4, 7], [5, 6]], \"1,2\": [[0, 7], [1, 6], [2, 5], [3, 4]]}. 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 524 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII has no row at P = 40 for the (3,8) family (its nearest lifts are 37), so there is no published value at this (n, k).",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 57087,
   "ris_trials_per_side": 524000000,
   "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 59705502, 2026-10-12), then 144 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 380 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 10."
  }
 }
}