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86, 134, 204 ], "Z": [ 19, 59, 86, 142, 176 ] }, { "X": [ 39, 58, 87, 135, 205 ], "Z": [ 18, 58, 85, 141, 175 ] }, { "X": [ 40, 59, 88, 136, 206 ], "Z": [ 17, 57, 84, 140, 174 ] }, { "X": [ 41, 60, 89, 137, 207 ], "Z": [ 16, 56, 125, 139, 173 ] }, { "X": [ 0, 61, 90, 138, 208 ], "Z": [ 15, 55, 124, 138, 172 ] }, { "X": [ 1, 62, 91, 139, 209 ], "Z": [ 14, 54, 123, 137, 171 ] }, { "X": [ 2, 63, 92, 140, 168 ], "Z": [ 13, 53, 122, 136, 170 ] }, { "X": [ 3, 64, 93, 141, 169 ], "Z": [ 12, 52, 121, 135, 169 ] }, { "X": [ 4, 65, 94, 142, 170 ], "Z": [ 11, 51, 120, 134, 168 ] } ] }, "distance": { "d": 9, "P": { "value": 9, "confidence": "upper_bound", "witness": { "X": [ 8, 11, 95, 169 ], "Z": [ 3, 7, 8, 48, 94, 98 ] } } }, "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=42. Exponent array E (rows a=0..2, columns l=0..9): [[19, 38, 1, 29, 16, 33, 15, 4, 34, 8], [40, 12, 41, 2, 38, 15, 24, 21, 21, 11], [37, 10, 18, 8, 31, 35, 25, 7, 39, 41]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 4], [1, 6], [2, 8], [3, 7], [5, 9]], \"0,2\": [[0, 7], [1, 8], [2, 4], [3, 9], [5, 6]], \"1,2\": [[0, 9], [1, 2], [3, 8], [4, 6], [5, 7]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 9 is the lightest Pauli logical found through 240 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII has no row at P = 42 for the (3,10) family (its nearest lifts are 38, 46), so there is no published value at this (n, k).", "model": "Claude Fable 5.1", "search_budget": { "candidates_screened": 9789, "ris_trials_per_side": 240000000, "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 1200 trials per template (Perlmutter job 59705503, 2026-10-12), then 60 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 180 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 9." } } }