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279, 282, 291, 297, 300, 303, 312 ] }, "Z": { "value": 60, "confidence": "upper_bound", "witness": [ 318, 327, 330, 333, 339, 348, 351, 354, 360, 369, 372, 375, 381, 390, 393, 396, 402, 411, 414, 417, 423, 432, 435, 438, 444, 453, 456, 459, 465, 474, 477, 480, 486, 495, 498, 501, 507, 516, 519, 522, 528, 537, 540, 543, 549, 558, 561, 564, 570, 579, 582, 585, 591, 600, 603, 606, 612, 621, 624, 627 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^315 - 1 with a(x) = x^15 + x^35 + x^40 + x^62 + x^86 + x^98 + x^126 + x^142 + x^185 + x^195 + x^205 + x^207 + x^239 + x^286 + x^295, b(x) = x^7 + x^12 + x^45 + x^60 + x^99 + x^167 + x^223 + x^251 + x^310; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-26", "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" }