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"upper_bound", "witness": [ 8, 12, 26, 30, 67, 71, 73, 76, 90, 96, 105, 114, 118, 132, 136, 173, 177, 179, 182, 196, 202, 211, 220, 224, 238, 242, 279, 283, 285, 288, 302, 308, 317, 318, 325, 329, 330, 336, 337, 339, 351, 352, 354, 363, 383, 385, 395, 396, 412, 424, 431, 435, 436, 442, 443, 445, 457, 458, 460, 469, 489, 491, 501, 502, 518, 530, 537, 541, 542, 548, 549, 551, 563, 564, 566, 575, 595, 597, 607, 608, 624 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_106 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^318 - 1 with a(x) = x^19 + x^39 + x^80 + x^107 + x^147 + x^151 + x^166 + x^222 + x^253 + x^308, b(x) = x^3 + x^6 + x^9 + x^37 + x^76 + x^113 + x^115 + x^174 + x^203 + x^239 + x^263 + x^297; 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" }