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} }, "Z": { "value": 81, "confidence": "upper_bound", "witness": [ 1, 8, 16, 18, 27, 33, 40, 41, 45, 49, 54, 64, 66, 71, 81, 83, 92, 94, 101, 109, 111, 120, 126, 133, 134, 138, 142, 147, 157, 159, 164, 174, 176, 185, 187, 194, 202, 204, 213, 219, 226, 227, 231, 235, 240, 250, 252, 257, 267, 269, 278, 279, 281, 304, 307, 308, 314, 331, 342, 351, 363, 372, 374, 397, 400, 401, 407, 424, 435, 444, 456, 465, 467, 490, 493, 494, 500, 517, 528, 537, 549 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 1, "tool": "norm-lift quotient bound, m' = 93, quotient weight 27", "survived_samples": 300000000 } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^279 - 1 with a(x) = x^3 + x^16 + x^18 + x^39 + x^55 + x^101 + x^120 + x^158 + x^208 + x^274, b(x) = x^21 + x^70 + x^79 + x^134 + x^149 + x^160 + x^173 + x^184 + x^193; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-22", "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" }