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[ 36, 55, 76, 130, 176 ], "Z": [ 37, 44, 84, 114, 153 ] }, { "X": [ 37, 56, 77, 131, 177 ], "Z": [ 36, 43, 83, 151, 152 ] }, { "X": [ 0, 57, 78, 132, 178 ], "Z": [ 35, 42, 82, 150, 189 ] }, { "X": [ 1, 58, 79, 133, 179 ], "Z": [ 34, 41, 81, 149, 188 ] }, { "X": [ 2, 59, 80, 134, 180 ], "Z": [ 33, 40, 80, 148, 187 ] }, { "X": [ 3, 60, 81, 135, 181 ], "Z": [ 32, 39, 79, 147, 186 ] }, { "X": [ 4, 61, 82, 136, 182 ], "Z": [ 31, 38, 78, 146, 185 ] }, { "X": [ 5, 62, 83, 137, 183 ], "Z": [ 30, 75, 77, 145, 184 ] }, { "X": [ 6, 63, 84, 138, 184 ], "Z": [ 29, 74, 76, 144, 183 ] }, { "X": [ 7, 64, 85, 139, 185 ], "Z": [ 28, 73, 113, 143, 182 ] }, { "X": [ 8, 65, 86, 140, 186 ], "Z": [ 27, 72, 112, 142, 181 ] } ] }, "distance": { "d": 8, "P": { "value": 8, "confidence": "upper_bound", "witness": { "X": [ 70, 122, 125, 161 ], "Z": [ 25, 37, 77, 188 ] } } }, "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=38. Exponent array E (rows a=0..2, columns l=0..9): [[23, 28, 11, 24, 9, 33, 33, 0, 29, 31], [24, 28, 34, 2, 22, 3, 20, 19, 19, 26], [29, 26, 10, 33, 27, 35, 11, 27, 3, 28]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 2], [1, 6], [3, 7], [4, 9], [5, 8]], \"0,2\": [[0, 7], [1, 8], [2, 4], [3, 9], [5, 6]], \"1,2\": [[0, 3], [1, 4], [2, 9], [5, 7], [6, 8]]}. 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 326 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the symplectic doubling (upper bound). The paper's Table VII lists [[190,78,9]] 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": 11016, "ris_trials_per_side": 326000000, "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 1500 trials per template (Perlmutter job 59705503, 2026-10-12), then 96 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 230 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 8." } } }