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"seeds": [ 0 ] } }, "Z": { "value": 78, "confidence": "upper_bound", "witness": [ 2, 9, 22, 55, 62, 67, 86, 90, 93, 110, 122, 124, 148, 164, 165, 168, 175, 188, 221, 228, 233, 252, 256, 259, 276, 288, 290, 314, 330, 331, 333, 345, 351, 355, 359, 364, 370, 374, 390, 393, 409, 411, 413, 423, 426, 435, 439, 447, 458, 462, 470, 474, 477, 487, 499, 511, 517, 521, 525, 530, 536, 540, 556, 559, 575, 577, 579, 589, 592, 601, 605, 613, 624, 628, 636, 640, 643, 653 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_166 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^332 - 1 with a(x) = x^95 + x^145 + x^154 + x^220 + x^267 + x^331, b(x) = x^34 + x^38 + x^47 + x^62 + x^98 + x^102; 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" }