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349, 411, 515, 586, 656 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "upper_bound", "witness": [ 35, 44, 63, 87, 93, 94, 154, 191, 200, 219, 254, 262, 276, 284, 346, 419, 450, 520, 521, 563 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 10000000, "seeds": [ 83000018600 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 70300000 } }, "Z": { "value": 20, "confidence": "upper_bound", "witness": [ 9, 18, 36, 65, 142, 146, 203, 250, 319, 342, 349, 435, 441, 471, 475, 565, 605, 617, 673, 697 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 10000000, "seeds": [ 83000018601 ], "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=89, n=8P=712, k=2P+4=182. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_89: E_x = [[74, 57, 77, 8, 35, 1, 19, 42], [48, 0, 70, 14, 10, 18, 13, 63], [64, 42, 75, 47, 10, 59, 2, 8]], E_z = [[67, 8, 78, 32, 28, 25, 20, 82], [0, 59, 3, 88, 51, 3, 35, 33], [87, 0, 20, 6, 33, 18, 36, 55]]. 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 -> 992 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 20, Z 20. 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 20 and 20; board fast pass (8,000,000 gf2_fast trials, pair depth 8) read 20 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\": 89, \"E\": [[74, 57, 77, 8, 35, 1, 19, 42], [48, 0, 70, 14, 10, 18, 13, 63], [64, 42, 75, 47, 10, 59, 2, 8]], \"D\": [[67, 8, 78, 32, 28, 25, 20, 82], [0, 59, 3, 88, 51, 3, 35, 33], [87, 0, 20, 6, 33, 18, 36, 55]]}" } }