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"X": { "value": 31, "confidence": "upper_bound", "witness": [ 35, 38, 63, 66, 69, 149, 152, 221, 224, 249, 252, 332, 335, 376, 387, 403, 414, 464, 491, 552, 563, 574, 579, 585, 596, 607, 618, 629, 651, 684, 706 ] }, "Z": { "value": 31, "confidence": "upper_bound", "witness": [ 32, 54, 87, 109, 120, 131, 142, 153, 159, 164, 175, 186, 247, 274, 324, 335, 351, 362, 403, 406, 486, 489, 514, 517, 586, 589, 669, 672, 675, 700, 703 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^369 - 1 with a(x) = x^162 + x^173 + x^250, b(x) = x^128 + x^314; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-21", "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" }