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98, 135, 196 ] }, { "X": [ 9, 40, 87, 158, 196 ], "Z": [ 36, 48, 97, 134, 195 ] }, { "X": [ 10, 41, 88, 159, 197 ], "Z": [ 35, 47, 96, 133, 194 ] }, { "X": [ 11, 42, 89, 120, 198 ], "Z": [ 34, 46, 95, 132, 193 ] }, { "X": [ 12, 43, 90, 121, 199 ], "Z": [ 33, 45, 94, 131, 192 ] }, { "X": [ 13, 44, 91, 122, 160 ], "Z": [ 32, 44, 93, 130, 191 ] }, { "X": [ 14, 45, 92, 123, 161 ], "Z": [ 31, 43, 92, 129, 190 ] }, { "X": [ 15, 46, 93, 124, 162 ], "Z": [ 30, 42, 91, 128, 189 ] }, { "X": [ 16, 47, 94, 125, 163 ], "Z": [ 29, 41, 90, 127, 188 ] }, { "X": [ 17, 48, 95, 126, 164 ], "Z": [ 28, 40, 89, 126, 187 ] }, { "X": [ 18, 49, 96, 127, 165 ], "Z": [ 27, 79, 88, 125, 186 ] }, { "X": [ 19, 50, 97, 128, 166 ], "Z": [ 26, 78, 87, 124, 185 ] }, { "X": [ 20, 51, 98, 129, 167 ], "Z": [ 25, 77, 86, 123, 184 ] } ] }, "distance": { "d": 19, "P": { "value": 19, "confidence": "upper_bound", "witness": { "X": [ 20, 31, 73, 74, 77, 88, 120, 154, 159, 165, 175, 186, 193 ], "Z": [ 6, 20, 70, 73, 77, 103, 120, 123, 154, 189, 192 ] } } }, "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "construction": "search", "date": "2026-10-13", "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=40. Exponent array E (rows a=0..3, columns l=0..9): [[12, 9, 32, 4, 39, 15, 8, 2, 21, 18], [25, 4, 12, 6, 3, 38, 32, 29, 0, 17], [9, 23, 39, 14, 28, 19, 33, 21, 28, 8], [19, 24, 28, 36, 21, 5, 30, 2, 32, 23]]. Off-diagonal pair partitions M: {\"0,1\": [[0, 3], [1, 7], [2, 8], [4, 6], [5, 9]], \"0,2\": [[0, 7], [1, 4], [2, 9], [3, 5], [6, 8]], \"0,3\": [[0, 5], [1, 2], [3, 7], [4, 8], [6, 9]], \"1,2\": [[0, 8], [1, 6], [2, 5], [3, 9], [4, 7]], \"1,3\": [[0, 9], [1, 8], [2, 4], [3, 6], [5, 7]], \"2,3\": [[0, 4], [1, 3], [2, 6], [5, 9], [7, 8]]}. The paper publishes no generators for its halved instances; this code is from a random search over the template. Distance 19 is the lightest Pauli-weight logical found by a 300,000-trial Pauli RIS screen, 100,000,000 gf2_fast trials on the symplectic doubling, and 456 random per-qubit symplectic frames x 1,000,000 gf2_fast trials (upper bound). The paper's table lists [[200,43,20]] for this P, which this search did not reach.", "search_budget": { "candidates_screened": 120, "ris_trials_per_side": 456000000, "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 (120 P=40 templates, 300,000 trials), 100,000,000 unframed gf2_fast trials, then 456 random per-qubit symplectic frames x 1,000,000 gf2_fast trials on the doubling (Perlmutter job 59676167, two replicas, 2026-10-11). Lightest Pauli-weight logical found: 19; no frame found lighter. Upper bound only." }, "model": "Claude Fable 5.1" } }