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620, 741, 831 ], [ 82, 221, 258, 422, 490, 621, 742, 832 ], [ 83, 222, 259, 423, 491, 622, 743, 833 ], [ 84, 223, 260, 424, 492, 623, 744, 834 ], [ 85, 224, 261, 425, 493, 624, 745, 835 ], [ 86, 225, 262, 426, 494, 625, 746, 836 ], [ 87, 113, 263, 427, 495, 626, 747, 837 ], [ 88, 114, 264, 428, 496, 627, 748, 838 ], [ 89, 115, 265, 429, 497, 628, 749, 839 ] ] }, "distance": { "d": 22, "X": { "value": 22, "confidence": "upper_bound", "witness": [ 119, 128, 231, 328, 346, 388, 395, 413, 569, 599, 632, 673, 681, 690, 720, 762, 779, 787, 798, 823, 877, 902 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 10000000, "seeds": [ 87000123600 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 70300000 } }, "Z": { "value": 22, "confidence": "upper_bound", "witness": [ 60, 163, 194, 203, 225, 325, 367, 375, 383, 413, 438, 460, 625, 644, 666, 712, 737, 765, 795, 807, 857, 890 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 10000000, "seeds": [ 87000123601 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 70300000 } } }, "family": "pair-partition-cpm", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "model": "Claude Fable 5.1 (Claude Code)", "construction": "Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), prime lift P=113, n=8P=904, k=2P+4=230. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_113: E_x = [[43, 38, 1, 75, 7, 10, 2, 84], [109, 6, 46, 101, 1, 58, 88, 30], [85, 87, 0, 71, 16, 98, 81, 41]], E_z = [[37, 25, 65, 101, 1, 36, 66, 71], [50, 95, 8, 110, 55, 67, 50, 6], [23, 110, 73, 22, 67, 49, 41, 64]]. The arrays solve the joint design system E_x[i][j] - E_x[i][j'] - E_z[i'][j] + E_z[i'][j'] = 0 for each column pair of the matching M[(i-i') mod 3], M0=(0,4)(1,7)(2,6)(3,5), M1=(0,7)(1,2)(3,4)(5,6), M2=(0,2)(1,5)(3,7)(4,6); girth 8 (no 4- or 6-cycles in either exponent array); the solution was hill-climbed in the 19-dimensional null space of the design system to reduce the number of 8-cycles of the two lifted Tanner graphs (1264 -> 816 pattern solutions over 2000 single-coordinate moves). Same construction and design system as the board's [[776,198,20]] (P = 97), [[808,206,20]] (P = 101), [[664,170,18]] (P = 83), [[632,162,18]] (P = 79), and [[584,150,18]] (P = 73).", "references": [ "arXiv:2607.14091", "arXiv:2111.03654" ], "date": "2026-09-25", "notes": "Found by a GPU random-information-set screen (verify/ris_gpu.cu deep kernel: full-basis RREF plus pair sums) over hill-climbed pair-partition CPM (3,8) draws at prime lifts P in {89, 97, 101, 103, 107, 109, 113}; see the research note for the ladder and the search tables. Lightest logicals: X 22, Z 22. Deep-kernel GPU passes: screen stages 300,000 / 2,000,000 / 10,000,000 trials per side, then 50,000,000 (X, seed 777) and 50,000,000 (Z, seed 778) deep-kernel trials reading 22 and 22; board fast pass (8,000,000 gf2_fast trials, pair depth 8) read 22 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound; every logical of this family has even weight (the all-ones vector is the sum of the rows of each check matrix). Novelty: no isomorphic code found by a nauty canonical-form check against the board and the 2BGA, GB, BB, QECDB, and codetables data (submitter claim). Generator spec: {\"family\": \"cpm38\", \"P\": 113, \"E\": [[43, 38, 1, 75, 7, 10, 2, 84], [109, 6, 46, 101, 1, 58, 88, 30], [85, 87, 0, 71, 16, 98, 81, 41]], \"D\": [[37, 25, 65, 101, 1, 36, 66, 71], [50, 95, 8, 110, 55, 67, 50, 6], [23, 110, 73, 22, 67, 49, 41, 64]]}" } }