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18, "confidence": "upper_bound", "witness": { "X": [ 17, 20, 24, 59, 66, 90, 144, 159, 175, 188, 200 ], "Z": [ 8, 20, 24, 41, 58, 68, 127, 142, 152 ] } } }, "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=44. Exponent array E (rows a=0..3, columns l=0..9): [[29, 29, 42, 43, 27, 30, 16, 4, 30, 17], [24, 1, 34, 35, 18, 16, 5, 27, 31, 0], [34, 30, 21, 13, 19, 36, 11, 33, 3, 25], [17, 17, 30, 3, 15, 3, 10, 13, 41, 0]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 8], [1, 7], [2, 3], [4, 6], [5, 9]], \"0,2\": [[0, 7], [1, 4], [2, 8], [3, 9], [5, 6]], \"0,3\": [[0, 1], [2, 5], [3, 6], [4, 8], [7, 9]], \"1,2\": [[0, 4], [1, 5], [2, 9], [3, 8], [6, 7]], \"1,3\": [[0, 9], [1, 6], [2, 7], [3, 4], [5, 8]], \"2,3\": [[0, 5], [1, 8], [2, 6], [3, 7], [4, 9]]}. 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 264 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 = 44 for the (4,10) family (its nearest lifts are 40, 43, 47, 49), so there is no published value at this (n, k).", "model": "Claude Fable 5.1", "search_budget": { "candidates_screened": 81689, "ris_trials_per_side": 264000000, "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 84 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: 18." } } }