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643, 653, 655, 656, 665, 666, 670, 682, 684 ] }, "Z": { "value": 110, "confidence": "upper_bound", "witness": [ 6, 8, 20, 24, 25, 34, 35, 37, 47, 50, 57, 59, 90, 95, 99, 111, 124, 125, 126, 131, 142, 143, 147, 153, 158, 168, 174, 178, 184, 185, 186, 191, 192, 200, 208, 216, 220, 223, 238, 244, 247, 265, 267, 281, 282, 289, 294, 295, 297, 307, 308, 313, 319, 331, 333, 338, 351, 356, 359, 360, 363, 367, 370, 374, 376, 400, 401, 404, 407, 409, 410, 413, 415, 416, 424, 426, 427, 429, 430, 436, 439, 444, 447, 455, 459, 478, 480, 506, 518, 525, 532, 557, 563, 576, 591, 592, 611, 613, 620, 625, 629, 630, 632, 633, 651, 661, 662, 665, 680, 685 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^345 - 1 with a(x) = x^157 + x^246 + x^293 + x^294 + x^296 + x^320 + x^321, b(x) = x^12 + x^30 + x^66 + x^89 + x^108 + x^144 + x^196 + x^198 + x^208 + x^221 + x^233 + x^280 + x^309 + x^318 + x^330; 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" }