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], "notes": "Halved CPM pair-partition code of arXiv:2609.30069 (Definition 1, reversing fold of Proposition 4) at (J,L)=(4,10), lift P=36. Exponent array E (rows a=0..3, columns l=0..9): [[34, 32, 18, 18, 9, 27, 33, 16, 14, 14], [18, 24, 30, 4, 4, 3, 34, 1, 20, 17], [5, 31, 21, 4, 10, 20, 23, 31, 8, 14], [23, 27, 7, 11, 19, 1, 8, 32, 5, 10]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 2], [1, 7], [3, 4], [5, 8], [6, 9]], \"0,2\": [[0, 4], [1, 5], [2, 9], [3, 7], [6, 8]], \"0,3\": [[0, 3], [1, 9], [2, 6], [4, 5], [7, 8]], \"1,2\": [[0, 5], [1, 6], [2, 8], [3, 9], [4, 7]], \"1,3\": [[0, 7], [1, 3], [2, 4], [5, 9], [6, 8]], \"2,3\": [[0, 2], [1, 8], [3, 4], [5, 7], [6, 9]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 16 is the lightest Pauli logical found through 378 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 = 36 for the (4,10) family (its nearest lifts are 30, 32, 34, 37, 40), so there is no published value at this (n, k).", "model": "Claude Fable 5.1", "search_budget": { "candidates_screened": 159088, "ris_trials_per_side": 378000000, "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 59705376, 2026-10-12), then 108 frames x 1,000,000 gf2_fast trials (jobs 59731365 to 59731368) and 270 further frames x 1,000,000 trials with fresh seeds (job 59779389, 2026-10-14). Lightest Pauli logical found: 16." } } }