{
 "schema_version": "0.4",
 "name": "[[110,25,12]] halved CPM pair-partition, (J,L)=(4,10), P=22",
 "code_type": "stabilizer",
 "n": 110,
 "k": 25,
 "checks": {
  "S": [
   {
    "X": [
     18,
     24,
     65,
     83,
     93
    ],
    "Z": [
     14,
     30,
     51,
     82,
     92
    ]
   },
   {
    "X": [
     19,
     25,
     44,
     84,
     94
    ],
    "Z": [
     13,
     29,
     50,
     81,
     91
    ]
   },
   {
    "X": [
     20,
     26,
     45,
     85,
     95
    ],
    "Z": [
     12,
     28,
     49,
     80,
     90
    ]
   },
   {
    "X": [
     21,
     27,
     46,
     86,
     96
    ],
    "Z": [
     11,
     27,
     48,
     79,
     89
    ]
   },
   {
    "X": [
     0,
     28,
     47,
     87,
     97
    ],
    "Z": [
     10,
     26,
     47,
     78,
     88
    ]
   },
   {
    "X": [
     1,
     29,
     48,
     66,
     98
    ],
    "Z": [
     9,
     25,
     46,
     77,
     109
    ]
   },
   {
    "X": [
     2,
     30,
     49,
     67,
     99
    ],
    "Z": [
     8,
     24,
     45,
     76,
     108
    ]
   },
   {
    "X": [
     3,
     31,
     50,
     68,
     100
    ],
    "Z": [
     7,
     23,
     44,
     75,
     107
    ]
   },
   {
    "X": [
     4,
     32,
     51,
     69,
     101
    ],
    "Z": [
     6,
     22,
     65,
     74,
     106
    ]
   },
   {
    "X": [
     5,
     33,
     52,
     70,
     102
    ],
    "Z": [
     5,
     43,
     64,
     73,
     105
    ]
   },
   {
    "X": [
     6,
     34,
     53,
     71,
     103
    ],
    "Z": [
     4,
     42,
     63,
     72,
     104
    ]
   },
   {
    "X": [
     7,
     35,
     54,
     72,
     104
    ],
    "Z": [
     3,
     41,
     62,
     71,
     103
    ]
   },
   {
    "X": [
     8,
     36,
     55,
     73,
     105
    ],
    "Z": [
     2,
     40,
     61,
     70,
     102
    ]
   },
   {
    "X": [
     9,
     37,
     56,
     74,
     106
    ],
    "Z": [
     1,
     39,
     60,
     69,
     101
    ]
   },
   {
    "X": [
     10,
     38,
     57,
     75,
     107
    ],
    "Z": [
     0,
     38,
     59,
     68,
     100
    ]
   },
   {
    "X": [
     11,
     39,
     58,
     76,
     108
    ],
    "Z": [
     21,
     37,
     58,
     67,
     99
    ]
   },
   {
    "X": [
     12,
     40,
     59,
     77,
     109
    ],
    "Z": [
     20,
     36,
     57,
     66,
     98
    ]
   },
   {
    "X": [
     13,
     41,
     60,
     78,
     88
    ],
    "Z": [
     19,
     35,
     56,
     87,
     97
    ]
   },
   {
    "X": [
     14,
     42,
     61,
     79,
     89
    ],
    "Z": [
     18,
     34,
     55,
     86,
     96
    ]
   },
   {
    "X": [
     15,
     43,
     62,
     80,
     90
    ],
    "Z": [
     17,
     33,
     54,
     85,
     95
    ]
   },
   {
    "X": [
     16,
     22,
     63,
     81,
     91
    ],
    "Z": [
     16,
     32,
     53,
     84,
     94
    ]
   },
   {
    "X": [
     17,
     23,
     64,
     82,
     92
    ],
    "Z": [
     15,
     31,
     52,
     83,
     93
    ]
   },
   {
    "X": [
     14,
     29,
     58,
     67,
     92
    ],
    "Z": [
     11,
     41,
     44,
     76,
     88
    ]
   },
   {
    "X": [
     15,
     30,
     59,
     68,
     93
    ],
    "Z": [
     10,
     40,
     65,
     75,
     109
    ]
   },
   {
    "X": [
     16,
     31,
     60,
     69,
     94
    ],
    "Z": [
     9,
     39,
     64,
     74,
     108
    ]
   },
   {
    "X": [
     17,
     32,
     61,
     70,
     95
    ],
    "Z": [
     8,
     38,
     63,
     73,
     107
    ]
   },
   {
    "X": [
     18,
     33,
     62,
     71,
     96
    ],
    "Z": [
     7,
     37,
     62,
     72,
     106
    ]
   },
   {
    "X": [
     19,
     34,
     63,
     72,
     97
    ],
    "Z": [
     6,
     36,
     61,
     71,
     105
    ]
   },
   {
    "X": [
     20,
     35,
     64,
     73,
     98
    ],
    "Z": [
     5,
     35,
     60,
     70,
     104
    ]
   },
   {
    "X": [
     21,
     36,
     65,
     74,
     99
    ],
    "Z": [
     4,
     34,
     59,
     69,
     103
    ]
   },
   {
    "X": [
     0,
     37,
     44,
     75,
     100
    ],
    "Z": [
     3,
     33,
     58,
     68,
     102
    ]
   },
   {
    "X": [
     1,
     38,
     45,
     76,
     101
    ],
    "Z": [
     2,
     32,
     57,
     67,
     101
    ]
   },
   {
    "X": [
     2,
     39,
     46,
     77,
     102
    ],
    "Z": [
     1,
     31,
     56,
     66,
     100
    ]
   },
   {
    "X": [
     3,
     40,
     47,
     78,
     103
    ],
    "Z": [
     0,
     30,
     55,
     87,
     99
    ]
   },
   {
    "X": [
     4,
     41,
     48,
     79,
     104
    ],
    "Z": [
     21,
     29,
     54,
     86,
     98
    ]
   },
   {
    "X": [
     5,
     42,
     49,
     80,
     105
    ],
    "Z": [
     20,
     28,
     53,
     85,
     97
    ]
   },
   {
    "X": [
     6,
     43,
     50,
     81,
     106
    ],
    "Z": [
     19,
     27,
     52,
     84,
     96
    ]
   },
   {
    "X": [
     7,
     22,
     51,
     82,
     107
    ],
    "Z": [
     18,
     26,
     51,
     83,
     95
    ]
   },
   {
    "X": [
     8,
     23,
     52,
     83,
     108
    ],
    "Z": [
     17,
     25,
     50,
     82,
     94
    ]
   },
   {
    "X": [
     9,
     24,
     53,
     84,
     109
    ],
    "Z": [
     16,
     24,
     49,
     81,
     93
    ]
   },
   {
    "X": [
     10,
     25,
     54,
     85,
     88
    ],
    "Z": [
     15,
     23,
     48,
     80,
     92
    ]
   },
   {
    "X": [
     11,
     26,
     55,
     86,
     89
    ],
    "Z": [
     14,
     22,
     47,
     79,
     91
    ]
   },
   {
    "X": [
     12,
     27,
     56,
     87,
     90
    ],
    "Z": [
     13,
     43,
     46,
     78,
     90
    ]
   },
   {
    "X": [
     13,
     28,
     57,
     66,
     91
    ],
    "Z": [
     12,
     42,
     45,
     77,
     89
    ]
   },
   {
    "X": [
     1,
     23,
     63,
     68,
     107
    ],
    "Z": [
     10,
     37,
     46,
     71,
     96
    ]
   },
   {
    "X": [
     2,
     24,
     64,
     69,
     108
    ],
    "Z": [
     9,
     36,
     45,
     70,
     95
    ]
   },
   {
    "X": [
     3,
     25,
     65,
     70,
     109
    ],
    "Z": [
     8,
     35,
     44,
     69,
     94
    ]
   },
   {
    "X": [
     4,
     26,
     44,
     71,
     88
    ],
    "Z": [
     7,
     34,
     65,
     68,
     93
    ]
   },
   {
    "X": [
     5,
     27,
     45,
     72,
     89
    ],
    "Z": [
     6,
     33,
     64,
     67,
     92
    ]
   },
   {
    "X": [
     6,
     28,
     46,
     73,
     90
    ],
    "Z": [
     5,
     32,
     63,
     66,
     91
    ]
   },
   {
    "X": [
     7,
     29,
     47,
     74,
     91
    ],
    "Z": [
     4,
     31,
     62,
     87,
     90
    ]
   },
   {
    "X": [
     8,
     30,
     48,
     75,
     92
    ],
    "Z": [
     3,
     30,
     61,
     86,
     89
    ]
   },
   {
    "X": [
     9,
     31,
     49,
     76,
     93
    ],
    "Z": [
     2,
     29,
     60,
     85,
     88
    ]
   },
   {
    "X": [
     10,
     32,
     50,
     77,
     94
    ],
    "Z": [
     1,
     28,
     59,
     84,
     109
    ]
   },
   {
    "X": [
     11,
     33,
     51,
     78,
     95
    ],
    "Z": [
     0,
     27,
     58,
     83,
     108
    ]
   },
   {
    "X": [
     12,
     34,
     52,
     79,
     96
    ],
    "Z": [
     21,
     26,
     57,
     82,
     107
    ]
   },
   {
    "X": [
     13,
     35,
     53,
     80,
     97
    ],
    "Z": [
     20,
     25,
     56,
     81,
     106
    ]
   },
   {
    "X": [
     14,
     36,
     54,
     81,
     98
    ],
    "Z": [
     19,
     24,
     55,
     80,
     105
    ]
   },
   {
    "X": [
     15,
     37,
     55,
     82,
     99
    ],
    "Z": [
     18,
     23,
     54,
     79,
     104
    ]
   },
   {
    "X": [
     16,
     38,
     56,
     83,
     100
    ],
    "Z": [
     17,
     22,
     53,
     78,
     103
    ]
   },
   {
    "X": [
     17,
     39,
     57,
     84,
     101
    ],
    "Z": [
     16,
     43,
     52,
     77,
     102
    ]
   },
   {
    "X": [
     18,
     40,
     58,
     85,
     102
    ],
    "Z": [
     15,
     42,
     51,
     76,
     101
    ]
   },
   {
    "X": [
     19,
     41,
     59,
     86,
     103
    ],
    "Z": [
     14,
     41,
     50,
     75,
     100
    ]
   },
   {
    "X": [
     20,
     42,
     60,
     87,
     104
    ],
    "Z": [
     13,
     40,
     49,
     74,
     99
    ]
   },
   {
    "X": [
     21,
     43,
     61,
     66,
     105
    ],
    "Z": [
     12,
     39,
     48,
     73,
     98
    ]
   },
   {
    "X": [
     0,
     22,
     62,
     67,
     106
    ],
    "Z": [
     11,
     38,
     47,
     72,
     97
    ]
   },
   {
    "X": [
     21,
     29,
     59,
     82,
     94
    ],
    "Z": [
     16,
     38,
     65,
     76,
     94
    ]
   },
   {
    "X": [
     0,
     30,
     60,
     83,
     95
    ],
    "Z": [
     15,
     37,
     64,
     75,
     93
    ]
   },
   {
    "X": [
     1,
     31,
     61,
     84,
     96
    ],
    "Z": [
     14,
     36,
     63,
     74,
     92
    ]
   },
   {
    "X": [
     2,
     32,
     62,
     85,
     97
    ],
    "Z": [
     13,
     35,
     62,
     73,
     91
    ]
   },
   {
    "X": [
     3,
     33,
     63,
     86,
     98
    ],
    "Z": [
     12,
     34,
     61,
     72,
     90
    ]
   },
   {
    "X": [
     4,
     34,
     64,
     87,
     99
    ],
    "Z": [
     11,
     33,
     60,
     71,
     89
    ]
   },
   {
    "X": [
     5,
     35,
     65,
     66,
     100
    ],
    "Z": [
     10,
     32,
     59,
     70,
     88
    ]
   },
   {
    "X": [
     6,
     36,
     44,
     67,
     101
    ],
    "Z": [
     9,
     31,
     58,
     69,
     109
    ]
   },
   {
    "X": [
     7,
     37,
     45,
     68,
     102
    ],
    "Z": [
     8,
     30,
     57,
     68,
     108
    ]
   },
   {
    "X": [
     8,
     38,
     46,
     69,
     103
    ],
    "Z": [
     7,
     29,
     56,
     67,
     107
    ]
   },
   {
    "X": [
     9,
     39,
     47,
     70,
     104
    ],
    "Z": [
     6,
     28,
     55,
     66,
     106
    ]
   },
   {
    "X": [
     10,
     40,
     48,
     71,
     105
    ],
    "Z": [
     5,
     27,
     54,
     87,
     105
    ]
   },
   {
    "X": [
     11,
     41,
     49,
     72,
     106
    ],
    "Z": [
     4,
     26,
     53,
     86,
     104
    ]
   },
   {
    "X": [
     12,
     42,
     50,
     73,
     107
    ],
    "Z": [
     3,
     25,
     52,
     85,
     103
    ]
   },
   {
    "X": [
     13,
     43,
     51,
     74,
     108
    ],
    "Z": [
     2,
     24,
     51,
     84,
     102
    ]
   },
   {
    "X": [
     14,
     22,
     52,
     75,
     109
    ],
    "Z": [
     1,
     23,
     50,
     83,
     101
    ]
   },
   {
    "X": [
     15,
     23,
     53,
     76,
     88
    ],
    "Z": [
     0,
     22,
     49,
     82,
     100
    ]
   },
   {
    "X": [
     16,
     24,
     54,
     77,
     89
    ],
    "Z": [
     21,
     43,
     48,
     81,
     99
    ]
   },
   {
    "X": [
     17,
     25,
     55,
     78,
     90
    ],
    "Z": [
     20,
     42,
     47,
     80,
     98
    ]
   },
   {
    "X": [
     18,
     26,
     56,
     79,
     91
    ],
    "Z": [
     19,
     41,
     46,
     79,
     97
    ]
   },
   {
    "X": [
     19,
     27,
     57,
     80,
     92
    ],
    "Z": [
     18,
     40,
     45,
     78,
     96
    ]
   },
   {
    "X": [
     20,
     28,
     58,
     81,
     93
    ],
    "Z": [
     17,
     39,
     44,
     77,
     95
    ]
   }
  ]
 },
 "distance": {
  "d": 12,
  "P": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     4,
     5,
     15,
     16,
     32,
     43,
     76,
     87,
     88,
     93,
     99,
     104
    ],
    "Z": [
     76,
     87,
     88,
     99
    ]
   }
  }
 },
 "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=22. Exponent array E (rows a=0..3, columns l=0..9): [[4, 14, 20, 8, 1, 7, 5, 16, 17, 4], [8, 11, 15, 19, 8, 0, 21, 10, 18, 0], [21, 10, 21, 15, 3, 2, 20, 5, 3, 8], [1, 16, 15, 16, 7, 21, 6, 10, 16, 6]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 6], [1, 9], [2, 8], [3, 4], [5, 7]], \"0,2\": [[0, 7], [1, 2], [3, 9], [4, 8], [5, 6]], \"0,3\": [[0, 9], [1, 6], [2, 5], [3, 8], [4, 7]], \"1,2\": [[0, 3], [1, 4], [2, 7], [5, 9], [6, 8]], \"1,3\": [[0, 8], [1, 3], [2, 6], [4, 5], [7, 9]], \"2,3\": [[0, 2], [1, 7], [3, 6], [4, 9], [5, 8]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 12 is the lightest Pauli logical found through 980 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[110,25,13]] at this lift, as an exact value; this search did not reach 13, so the entry is 1 short of the published value.",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 291832,
   "ris_trials_per_side": 980000000,
   "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 3000 trials per template (Perlmutter job 59705375, 2026-10-12), then 300 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 680 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 12."
  }
 }
}