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65, "confidence": "upper_bound", "witness": [ 4, 12, 34, 41, 48, 58, 60, 75, 89, 92, 97, 98, 100, 113, 136, 141, 164, 165, 169, 179, 182, 190, 191, 201, 210, 216, 226, 227, 230, 232, 235, 252, 256, 259, 260, 271, 277, 289, 298, 309, 314, 317, 318, 323, 336, 341, 343, 358, 360, 362, 365, 369, 374, 387, 390, 392, 399, 401, 416, 422, 431, 450, 453, 455, 458 ] }, "Z": { "value": 65, "confidence": "upper_bound", "witness": [ 8, 11, 13, 16, 35, 44, 50, 65, 67, 74, 76, 79, 92, 97, 101, 104, 106, 108, 123, 125, 130, 143, 148, 149, 152, 157, 168, 177, 189, 195, 206, 207, 210, 214, 231, 234, 236, 239, 240, 250, 256, 265, 275, 276, 284, 287, 297, 301, 302, 325, 330, 353, 366, 368, 369, 374, 377, 391, 406, 408, 418, 425, 432, 454, 462 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^233 - 1 with a(x) = x^4 + x^43 + x^46 + x^112 + x^128 + x^132 + x^190 + x^226, b(x) = x^24 + x^56 + x^63 + x^69 + x^136 + x^150 + x^179 + x^190 + x^194 + x^216; 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" }