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627, 631, 636, 643 ] }, "Z": { "value": 101, "confidence": "upper_bound", "witness": [ 0, 2, 7, 8, 15, 20, 27, 30, 34, 39, 41, 50, 55, 63, 65, 67, 68, 70, 72, 73, 74, 75, 80, 82, 93, 98, 99, 100, 101, 111, 116, 121, 123, 130, 134, 135, 143, 156, 159, 160, 161, 170, 171, 172, 175, 176, 177, 180, 183, 184, 186, 187, 189, 190, 197, 201, 209, 215, 220, 222, 226, 228, 235, 240, 242, 246, 247, 250, 256, 258, 275, 282, 288, 290, 293, 294, 299, 301, 305, 307, 315, 316, 320, 321, 325, 332, 368, 399, 477, 478, 493, 517, 524, 541, 556, 566, 573, 594, 620, 628, 642 ], "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^323 - 1 with a(x) = x^56 + x^113 + x^163 + x^170 + x^178 + x^228, b(x) = x^8 + x^37 + x^42 + x^67 + x^98 + x^164 + x^188 + x^205; 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" }