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     121
    ]
   }
  ]
 },
 "distance": {
  "d": 13,
  "P": {
   "value": 13,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     79,
     81,
     83,
     85,
     87,
     89,
     91,
     93,
     95,
     97,
     99,
     101,
     103
    ],
    "Z": [
     79,
     81,
     83,
     85,
     87,
     89,
     91,
     93,
     95,
     97,
     99,
     101,
     103
    ]
   }
  }
 },
 "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=26. Exponent array E (rows a=0..3, columns l=0..9): [[18, 20, 22, 24, 1, 19, 3, 5, 14, 15], [1, 8, 6, 4, 8, 20, 25, 17, 5, 13], [20, 1, 13, 9, 21, 20, 0, 18, 4, 23], [2, 7, 17, 16, 6, 14, 17, 1, 23, 16]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 2], [1, 4], [3, 7], [5, 8], [6, 9]], \"0,2\": [[0, 9], [1, 5], [2, 7], [3, 8], [4, 6]], \"0,3\": [[0, 5], [1, 7], [2, 9], [3, 4], [6, 8]], \"1,2\": [[0, 1], [2, 5], [3, 6], [4, 8], [7, 9]], \"1,3\": [[0, 7], [1, 9], [2, 4], [3, 8], [5, 6]], \"2,3\": [[0, 6], [1, 2], [3, 5], [4, 7], [8, 9]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 13 is the lightest Pauli logical found through 716 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[130,29,14]] at this lift, as an exact value; this search did not reach 14, so the entry is 1 short of the published value.",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 223445,
   "ris_trials_per_side": 716000000,
   "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 2000 trials per template (Perlmutter job 59705375, 2026-10-12), then 216 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 500 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 13."
  }
 }
}