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132, 137, 143, 148, 154, 159, 165, 170, 176, 181, 187, 192, 198, 203, 209, 214, 220, 225 ] }, "Z": { "value": 42, "confidence": "upper_bound", "witness": [ 231, 237, 242, 248, 253, 259, 264, 270, 275, 281, 286, 292, 297, 303, 308, 314, 319, 325, 330, 336, 341, 347, 352, 358, 363, 369, 374, 380, 385, 391, 396, 402, 407, 413, 418, 424, 429, 435, 440, 446, 451, 457 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^231 - 1 with a(x) = x^18 + x^30 + x^32 + x^47 + x^52 + x^63 + x^70 + x^99 + x^163 + x^177 + x^189 + x^203 + x^204, b(x) = x^1 + x^7 + x^10 + x^71 + x^81 + x^118 + x^163 + x^176 + x^204 + x^212 + x^222; 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" }