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[ 0, 4, 8, 34, 44, 48, 49, 53, 57, 97, 98, 101, 102, 106, 110, 136, 146, 150, 151, 155, 159, 199, 200, 203, 204, 208, 212, 238, 248, 252, 253, 257, 261, 301, 302, 305, 326, 335, 339, 343, 347, 375, 379, 388, 392, 396, 428, 437, 441, 445, 449, 477, 481, 490, 494, 498, 530, 539, 543, 547, 551, 579, 583, 592, 596, 600 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_102 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 66, "confidence": "upper_bound", "witness": [ 12, 16, 20, 29, 33, 61, 65, 69, 73, 82, 114, 118, 122, 131, 135, 163, 167, 171, 175, 184, 216, 220, 224, 233, 237, 265, 269, 273, 277, 286, 306, 307, 310, 311, 351, 355, 359, 360, 364, 374, 400, 404, 408, 409, 412, 413, 453, 457, 461, 462, 466, 476, 502, 506, 510, 511, 514, 515, 555, 559, 563, 564, 568, 578, 604, 608 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_102 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^306 - 1 with a(x) = x^18 + x^26 + x^163 + x^174 + x^212 + x^239, b(x) = x^3 + x^68 + x^91 + x^149 + x^247 + x^251 + x^295 + x^304; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-23", "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" }