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"d": 98, "X": { "value": 98, "confidence": "upper_bound", "witness": [ 9, 10, 12, 32, 33, 40, 49, 59, 60, 62, 82, 83, 90, 99, 109, 110, 112, 132, 133, 140, 149, 159, 160, 162, 182, 183, 190, 199, 209, 210, 212, 232, 233, 240, 249, 259, 260, 262, 282, 283, 290, 299, 309, 310, 312, 332, 333, 340, 349, 350, 358, 372, 386, 387, 396, 397, 400, 408, 422, 436, 437, 446, 447, 450, 458, 472, 486, 487, 496, 497, 500, 508, 522, 536, 537, 546, 547, 550, 558, 572, 586, 587, 596, 597, 600, 608, 622, 636, 637, 646, 647, 650, 658, 672, 686, 687, 696, 697 ] }, "Z": { "value": 98, "confidence": "upper_bound", "witness": [ 0, 3, 4, 13, 14, 28, 42, 50, 53, 54, 63, 64, 78, 92, 100, 103, 104, 113, 114, 128, 142, 150, 153, 154, 163, 164, 178, 192, 200, 203, 204, 213, 214, 228, 242, 250, 253, 254, 263, 264, 278, 292, 300, 303, 304, 313, 314, 328, 342, 351, 360, 367, 368, 388, 390, 391, 401, 410, 417, 418, 438, 440, 441, 451, 460, 467, 468, 488, 490, 491, 501, 510, 517, 518, 538, 540, 541, 551, 560, 567, 568, 588, 590, 591, 601, 610, 617, 618, 638, 640, 641, 651, 660, 667, 668, 688, 690, 691 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^350 - 1 with a(x) = x^32 + x^81 + x^101 + x^143 + x^156 + x^169 + x^245 + x^249 + x^278 + x^279 + x^283, b(x) = x^11 + x^21 + x^136 + x^209 + x^212 + x^260 + x^348; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-28", "notes": "Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed." }, "family": "generalized-bicycle" }