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318, 339, 352, 391, 414, 424 ] ] }, "distance": { "d": 70, "X": { "value": 70, "confidence": "upper_bound", "witness": [ 1, 11, 14, 25, 32, 33, 43, 59, 62, 65, 67, 92, 103, 106, 113, 115, 139, 163, 178, 179, 202, 203, 206, 210, 211, 213, 215, 221, 226, 229, 239, 241, 253, 264, 265, 269, 275, 278, 279, 285, 288, 291, 300, 301, 305, 317, 319, 328, 330, 337, 349, 359, 363, 364, 368, 378, 389, 392, 395, 398, 406, 410, 412, 414, 422, 430, 432, 433, 436, 442 ] }, "Z": { "value": 70, "confidence": "upper_bound", "witness": [ 48, 54, 57, 58, 60, 68, 76, 78, 80, 84, 92, 95, 98, 101, 112, 122, 126, 127, 131, 141, 153, 160, 162, 171, 173, 185, 189, 190, 199, 202, 205, 211, 212, 215, 221, 225, 226, 237, 249, 251, 261, 264, 269, 275, 277, 279, 280, 284, 287, 288, 311, 312, 327, 351, 375, 377, 384, 387, 398, 423, 425, 428, 431, 447, 457, 458, 465, 476, 479, 489 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^245 - 1 with a(x) = x^65 + x^75 + x^98 + x^137 + x^150 + x^171 + x^192 + x^204 + x^205 + x^212 + x^230, b(x) = x^16 + x^44 + x^46 + x^62 + x^69 + x^88 + x^126 + x^133 + x^136 + x^145 + x^148 + x^149 + x^174 + x^182 + x^189 + x^211 + x^214 + x^222 + x^231 + x^236 + x^239; 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" }