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307, 308, 312 ] }, "Z": { "value": 90, "confidence": "upper_bound", "witness": [ 315, 318, 322, 323, 328, 329, 333, 336, 338, 348, 350, 353, 357, 358, 363, 364, 368, 371, 373, 383, 385, 388, 392, 393, 398, 399, 403, 406, 408, 418, 420, 423, 427, 428, 433, 434, 438, 441, 443, 453, 455, 458, 462, 463, 468, 469, 473, 476, 478, 488, 490, 493, 497, 498, 503, 504, 508, 511, 513, 523, 525, 528, 532, 533, 538, 539, 543, 546, 548, 558, 560, 563, 567, 568, 573, 574, 578, 581, 583, 593, 595, 598, 602, 603, 608, 609, 613, 616, 618, 628 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^315 - 1 with a(x) = x^49 + x^58 + x^86 + x^88 + x^100 + x^127 + x^143 + x^167 + x^257, b(x) = x^13 + x^83 + x^122 + x^167 + x^183 + x^240 + x^263 + x^264 + x^266 + x^272 + x^293; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-25", "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" }