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182, 233 ], "Z": [ 2, 94, 106, 178, 216 ] }, { "X": [ 24, 65, 142, 183, 234 ], "Z": [ 1, 93, 105, 177, 215 ] } ] }, "distance": { "d": 18, "P": { "value": 18, "confidence": "upper_bound", "witness": { "X": [ 22, 33, 70, 82, 93, 99, 130, 137, 151, 162, 194, 204, 215 ], "Z": [ 45, 82, 100, 109, 120, 152, 162 ] } } }, "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=48. Exponent array E (rows a=0..3, columns l=0..9): [[15, 15, 4, 35, 7, 16, 41, 30, 3, 43], [43, 43, 43, 26, 0, 17, 6, 31, 21, 33], [22, 31, 33, 31, 21, 28, 45, 5, 32, 17], [23, 0, 30, 44, 1, 8, 8, 32, 5, 22]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 1], [2, 3], [4, 6], [5, 9], [7, 8]], \"0,2\": [[0, 6], [1, 5], [2, 4], [3, 8], [7, 9]], \"0,3\": [[0, 4], [1, 7], [2, 9], [3, 5], [6, 8]], \"1,2\": [[0, 2], [1, 9], [3, 6], [4, 7], [5, 8]], \"1,3\": [[0, 8], [1, 5], [2, 7], [3, 4], [6, 9]], \"2,3\": [[0, 9], [1, 8], [2, 5], [3, 7], [4, 6]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 18 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 has no row at P = 48 for the (4,10) family (its nearest lifts are 43, 47, 49), so there is no published value at this (n, k).", "model": "Claude Fable 5.1", "search_budget": { "candidates_screened": 84899, "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 800 trials per template (Perlmutter job 59705376, 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: 18." } } }