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470, 541, 696, 735 ], [ 18, 111, 292, 377, 471, 542, 697, 736 ], [ 19, 112, 293, 378, 472, 543, 698, 737 ], [ 20, 113, 294, 379, 473, 544, 699, 738 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "upper_bound", "witness": [ 54, 81, 85, 93, 186, 241, 277, 330, 392, 420, 456, 482, 486, 508, 577, 596, 632, 659, 747, 771 ] }, "Z": { "value": 20, "confidence": "upper_bound", "witness": [ 25, 48, 57, 97, 221, 270, 299, 303, 332, 391, 449, 478, 481, 494, 576, 585, 598, 626, 675, 704 ] } }, "provenance": { "authors": [ "@pandey-tushar" ], "origin": "submission", "novelty": "unknown", "construction": "Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), prime lift P=101, n=8P=808, k=2P+4=206. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_101: E_x = [[37, 25, 46, 33, 40, 50, 97, 26], [61, 87, 90, 30, 63, 60, 39, 75], [56, 59, 72, 97, 7, 33, 71, 40]], E_z = [[88, 0, 3, 58, 91, 75, 54, 1], [78, 74, 87, 69, 80, 99, 36, 62], [80, 88, 8, 24, 31, 61, 7, 69]]. 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 {j,j'} 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).", "model": "Claude Opus 5", "references": [ "arXiv:2607.14091" ], "date": "2026-09-18", "notes": "Same pair-partition CPM construction as the board's [[584,150,18]] (P=73, published), [[632,162,18]] (P=79) and [[664,170,18]] (P=83), at prime lift P=101 (n=808), which the n<=1000 / w<=8 / d<=40 blocklength rule admits. Distance is a witness-backed upper bound: accelerated RIS ladder 2k, 20k, 200k and 1M trials all at 20. The trusted candidate gate reported no exact duplicate and no WL-equivalent board entry. Literature novelty of these parameters is unverified." }, "family": "pair-partition-cpm" }