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"witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 1, "tool": "norm-lift quotient bound, m' = 77, quotient weight 20", "survived_samples": 300000000 } }, "Z": { "value": 60, "confidence": "upper_bound", "witness": [ 6, 17, 32, 33, 40, 49, 53, 66, 67, 72, 83, 94, 109, 110, 117, 126, 130, 143, 144, 149, 160, 171, 186, 187, 194, 203, 207, 220, 221, 226, 233, 238, 242, 253, 258, 259, 260, 270, 282, 302, 310, 315, 319, 330, 335, 336, 337, 347, 359, 379, 387, 392, 396, 407, 412, 413, 414, 424, 436, 456 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 1, "tool": "norm-lift quotient bound, m' = 77, quotient weight 20", "survived_samples": 300000000 } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^231 - 1 with a(x) = x^5 + x^12 + x^105 + x^135 + x^147 + x^165 + x^182 + x^217 + x^218, b(x) = x^57 + x^59 + x^60 + x^71 + x^78 + x^95 + x^120 + x^156 + x^208; 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. Distance corrected from 68 to 66: the verifier found a weight-66 X-logical. The Z witness is its reflection under x -> x^-1, which maps an X-logical of a cyclic generalized-bicycle code to a Z-logical of equal weight." }, "family": "generalized-bicycle" }