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     113
    ]
   },
   {
    "X": [
     16,
     32,
     81,
     109,
     112
    ],
    "Z": [
     14,
     37,
     83,
     100,
     112
    ]
   },
   {
    "X": [
     17,
     33,
     82,
     110,
     113
    ],
    "Z": [
     13,
     36,
     82,
     99,
     139
    ]
   },
   {
    "X": [
     18,
     34,
     83,
     111,
     114
    ],
    "Z": [
     12,
     35,
     81,
     98,
     138
    ]
   },
   {
    "X": [
     19,
     35,
     56,
     84,
     115
    ],
    "Z": [
     11,
     34,
     80,
     97,
     137
    ]
   },
   {
    "X": [
     20,
     36,
     57,
     85,
     116
    ],
    "Z": [
     10,
     33,
     79,
     96,
     136
    ]
   },
   {
    "X": [
     21,
     37,
     58,
     86,
     117
    ],
    "Z": [
     9,
     32,
     78,
     95,
     135
    ]
   },
   {
    "X": [
     22,
     38,
     59,
     87,
     118
    ],
    "Z": [
     8,
     31,
     77,
     94,
     134
    ]
   },
   {
    "X": [
     23,
     39,
     60,
     88,
     119
    ],
    "Z": [
     7,
     30,
     76,
     93,
     133
    ]
   }
  ]
 },
 "distance": {
  "d": 14,
  "P": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     10,
     26,
     35,
     55,
     80,
     98,
     105,
     126,
     133,
     136
    ],
    "Z": [
     11,
     12,
     26,
     35,
     97,
     105,
     119,
     126
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "origin": "submission",
  "construction": "search",
  "date": "2026-10-13",
  "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=28. Exponent array E (rows a=0..3, columns l=0..9): [[13, 4, 27, 3, 17, 8, 19, 4, 8, 11], [4, 12, 15, 21, 10, 17, 2, 17, 9, 17], [23, 22, 14, 5, 24, 3, 3, 26, 9, 19], [4, 6, 16, 1, 23, 19, 23, 8, 20, 20]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 8], [1, 6], [2, 9], [3, 5], [4, 7]], \"0,2\": [[0, 7], [1, 8], [2, 5], [3, 6], [4, 9]], \"0,3\": [[0, 3], [1, 4], [2, 8], [5, 9], [6, 7]], \"1,2\": [[0, 9], [1, 3], [2, 7], [4, 5], [6, 8]], \"1,3\": [[0, 6], [1, 2], [3, 9], [4, 8], [5, 7]], \"2,3\": [[0, 8], [1, 5], [2, 4], [3, 7], [6, 9]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 14 is the lightest logical found in 1000000 refutation trials (upper bound). The paper's table lists [[140,31,15]] for this P, which this search did not reach.",
  "search_budget": {
   "candidates_screened": 120,
   "ris_trials_per_side": 408000000,
   "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, then 408 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the doubling (Perlmutter job 59676168, 2026-10-11). Lightest Pauli-weight logical found: 14; no frame found lighter. Upper bound only."
  },
  "model": "Claude Fable 5.1"
 }
}