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220, 223, 227, 228, 233, 234, 238, 241, 243 ] }, "Z": { "value": 70, "confidence": "upper_bound", "witness": [ 247, 249, 252, 256, 257, 262, 263, 267, 270, 272, 282, 284, 287, 291, 292, 297, 298, 302, 305, 307, 317, 319, 322, 326, 327, 332, 333, 337, 340, 342, 352, 354, 357, 361, 362, 367, 368, 372, 375, 377, 387, 389, 392, 396, 397, 402, 403, 407, 410, 412, 422, 424, 427, 431, 432, 437, 438, 442, 445, 447, 457, 459, 462, 466, 467, 472, 473, 477, 480, 482 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^245 - 1 with a(x) = x^12 + x^17 + x^35 + x^48 + x^81 + x^89 + x^170 + x^218 + x^225 + x^232 + x^243, b(x) = x^13 + x^18 + x^34 + x^40 + x^42 + x^54 + x^58 + x^81 + x^91 + x^113 + x^151 + x^168 + x^204 + x^225 + x^229 + x^230 + x^234; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-24", "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" }