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219 ], "Z": [ 34, 47, 116, 146, 227 ] }, { "X": [ 16, 88, 92, 162, 220 ], "Z": [ 33, 46, 115, 145, 226 ] }, { "X": [ 17, 89, 93, 163, 221 ], "Z": [ 32, 91, 114, 144, 225 ] }, { "X": [ 18, 90, 94, 164, 222 ], "Z": [ 31, 90, 113, 143, 224 ] }, { "X": [ 19, 91, 95, 165, 223 ], "Z": [ 30, 89, 112, 142, 223 ] }, { "X": [ 20, 46, 96, 166, 224 ], "Z": [ 29, 88, 111, 141, 222 ] }, { "X": [ 21, 47, 97, 167, 225 ], "Z": [ 28, 87, 110, 140, 221 ] } ] }, "distance": { "d": 8, "P": { "value": 8, "confidence": "upper_bound", "witness": { "X": [ 13, 79, 129, 148, 217, 229 ], "Z": [ 55, 148, 182, 229 ] } } }, "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)=(3,10), lift P=46. Exponent array E (rows a=0..2, columns l=0..9): [[9, 23, 35, 23, 19, 27, 5, 13, 16, 43], [30, 41, 27, 18, 45, 27, 32, 41, 29, 29], [24, 27, 44, 40, 40, 17, 16, 1, 4, 36]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 3], [1, 2], [4, 6], [5, 9], [7, 8]], \"0,2\": [[0, 4], [1, 9], [2, 7], [3, 5], [6, 8]], \"1,2\": [[0, 7], [1, 8], [2, 5], [3, 4], [6, 9]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 8 is the lightest Pauli logical found through 220 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[230,94,10]] at this lift under the plain fold, as an exact value; this entry uses the reversing fold, for which the table has no row at this lift.", "model": "Claude Fable 5.1", "search_budget": { "candidates_screened": 8107, "ris_trials_per_side": 220000000, "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 1000 trials per template (Perlmutter job 59705503, 2026-10-12), then 60 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 160 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 8." } } }