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234, 240, 287, 320, 323, 344, 449, 488, 510, 525, 550 ], [ 37, 48, 91, 167, 226, 235, 241, 288, 321, 324, 345, 450, 489, 511, 526, 551 ] ] }, "distance": { "d": 80, "X": { "value": 80, "confidence": "upper_bound", "witness": [ 4, 8, 18, 20, 23, 35, 41, 43, 56, 57, 61, 66, 73, 78, 82, 92, 94, 97, 109, 115, 117, 130, 131, 135, 140, 147, 152, 156, 166, 168, 171, 183, 189, 191, 204, 205, 209, 214, 221, 226, 230, 240, 242, 245, 257, 263, 265, 278, 279, 283, 288, 295, 301, 312, 319, 338, 344, 346, 358, 375, 386, 393, 412, 418, 420, 432, 449, 460, 467, 486, 492, 494, 506, 523, 534, 541, 560, 566, 568, 580 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 1, "tool": "norm-lift quotient bound, m' = 74, quotient weight 20", "survived_samples": 300000000 } }, "Z": { "value": 80, "confidence": "upper_bound", "witness": [ 11, 12, 18, 30, 36, 49, 50, 85, 86, 92, 104, 110, 123, 124, 159, 160, 166, 178, 184, 197, 198, 233, 234, 240, 252, 258, 271, 272, 300, 301, 302, 311, 323, 326, 329, 330, 333, 336, 361, 364, 367, 374, 375, 376, 385, 397, 400, 403, 404, 407, 410, 435, 438, 441, 448, 449, 450, 459, 471, 474, 477, 478, 481, 484, 509, 512, 515, 522, 523, 524, 533, 545, 548, 551, 552, 555, 558, 583, 586, 589 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 1, "tool": "norm-lift quotient bound, m' = 74, quotient weight 20", "survived_samples": 300000000 } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^296 - 1 with a(x) = x^40 + x^65 + x^80 + x^102 + x^141 + x^246 + x^267 + x^270, b(x) = x^7 + x^54 + x^60 + x^69 + x^128 + x^204 + x^247 + x^258; 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" }