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    "X": [
     18,
     48,
     52,
     80,
     113,
     125
    ],
    "Z": [
     16,
     37,
     74,
     94,
     119,
     129
    ]
   },
   {
    "X": [
     19,
     49,
     53,
     81,
     114,
     126
    ],
    "Z": [
     15,
     36,
     73,
     93,
     118,
     128
    ]
   },
   {
    "X": [
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     25,
     54,
     82,
     115,
     127
    ],
    "Z": [
     14,
     35,
     72,
     92,
     117,
     127
    ]
   },
   {
    "X": [
     21,
     26,
     55,
     83,
     116,
     128
    ],
    "Z": [
     13,
     34,
     71,
     91,
     116,
     126
    ]
   },
   {
    "X": [
     22,
     27,
     56,
     84,
     117,
     129
    ],
    "Z": [
     12,
     33,
     70,
     90,
     115,
     125
    ]
   },
   {
    "X": [
     23,
     28,
     57,
     85,
     118,
     130
    ],
    "Z": [
     11,
     32,
     69,
     89,
     114,
     149
    ]
   },
   {
    "X": [
     24,
     29,
     58,
     86,
     119,
     131
    ],
    "Z": [
     10,
     31,
     68,
     88,
     113,
     148
    ]
   },
   {
    "X": [
     0,
     30,
     59,
     87,
     120,
     132
    ],
    "Z": [
     9,
     30,
     67,
     87,
     112,
     147
    ]
   }
  ]
 },
 "distance": {
  "d": 11,
  "P": {
   "value": 11,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     21,
     41,
     58,
     78,
     124,
     133
    ],
    "Z": [
     21,
     25,
     54,
     64,
     116,
     137
    ]
   }
  }
 },
 "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=25. Exponent array E (rows a=0..3, columns l=0..11): [[18, 17, 18, 1, 10, 5, 2, 21, 5, 9, 12, 5], [12, 0, 2, 1, 15, 18, 22, 2, 3, 7, 15, 7], [11, 5, 9, 10, 18, 5, 14, 13, 9, 9, 13, 2], [24, 8, 19, 4, 15, 16, 12, 11, 4, 11, 17, 21]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 7], [1, 6], [2, 10], [3, 4], [5, 11], [8, 9]], \"0,2\": [[0, 5], [1, 2], [3, 7], [4, 6], [8, 10], [9, 11]], \"0,3\": [[0, 4], [1, 8], [2, 11], [3, 5], [6, 9], [7, 10]], \"1,2\": [[0, 10], [1, 5], [2, 8], [3, 6], [4, 11], [7, 9]], \"1,3\": [[0, 3], [1, 11], [2, 4], [5, 6], [7, 8], [9, 10]], \"2,3\": [[0, 11], [1, 3], [2, 9], [4, 10], [5, 8], [6, 7]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 11 is the lightest Pauli logical found through 454 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[150,53,12]] at this lift, as an exact value; this search did not reach 12, so the entry is 1 short of the published value.",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 25697,
   "ris_trials_per_side": 454000000,
   "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 59705503, 2026-10-12), then 144 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 310 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 11."
  }
 }
}