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"X": { "value": 81, "confidence": "upper_bound", "witness": [ 1, 2, 19, 21, 31, 35, 36, 39, 41, 57, 59, 61, 70, 91, 96, 109, 110, 116, 128, 131, 137, 162, 168, 172, 175, 177, 182, 199, 200, 205, 217, 218, 219, 227, 247, 254, 281, 289, 291, 294, 296, 314, 316, 329, 334, 360, 379, 384, 394, 402, 412, 422, 437, 448, 455, 478, 481, 483, 486, 495, 498, 505, 517, 528, 537, 557, 567, 569, 583, 599, 615, 619, 624, 626, 634, 648, 649, 650, 663, 665, 685 ] }, "Z": { "value": 79, "confidence": "upper_bound", "witness": [ 0, 2, 4, 7, 24, 33, 35, 38, 42, 45, 54, 57, 59, 64, 68, 76, 87, 92, 97, 100, 104, 123, 125, 128, 130, 133, 137, 142, 152, 156, 159, 163, 166, 168, 189, 190, 192, 194, 201, 202, 204, 206, 209, 216, 220, 228, 232, 235, 239, 242, 244, 246, 249, 268, 273, 282, 285, 287, 292, 294, 296, 299, 304, 322, 323, 325, 330, 332, 344, 350, 379, 385, 455, 562, 590, 595, 605, 671, 697 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 300000000, "survived_samples": 300000000, "tool": "verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified)", "seeds": [ 4102 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^349 - 1 with a(x) = x^58 + x^134 + x^184 + x^305, b(x) = x^29 + x^103 + x^323 + x^343; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-22", "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" }