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298, 306, 308, 309, 333, 335, 342, 345, 349, 351, 368, 371, 381, 389, 391, 392, 416, 418, 425, 428, 432, 434, 451, 454, 464, 472, 474, 475 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_83 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 63, "confidence": "upper_bound", "witness": [ 23, 24, 26, 34, 44, 47, 64, 66, 70, 73, 80, 82, 106, 107, 109, 117, 127, 130, 147, 149, 153, 156, 163, 165, 189, 190, 192, 200, 210, 213, 230, 232, 236, 239, 246, 248, 253, 276, 281, 290, 301, 304, 309, 321, 331, 336, 359, 364, 373, 384, 387, 392, 404, 414, 419, 442, 447, 456, 467, 470, 475, 487, 497 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_83 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^249 - 1 with a(x) = x^21 + x^57 + x^60 + x^69 + x^84 + x^120 + x^156 + x^160 + x^162 + x^165 + x^208 + x^237 + x^240 + x^243, b(x) = x^64 + x^90 + x^106 + x^139 + x^163 + x^171; 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" }