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"tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1602626403 ], "survived_samples": 300000000 } }, "Z": { "value": 30, "confidence": "upper_bound", "witness": [ 2, 5, 8, 11, 26, 29, 38, 41, 44, 47, 56, 59, 62, 65, 68, 71, 74, 77, 86, 89, 98, 101, 122, 125, 140, 143, 146, 149, 152, 155 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-27", "found_at_samples": 300000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1602626403 ], "survived_samples": 300000000 } } }, "provenance": { "authors": [ "@vprusso" ], "model": "Claude Fable 5.1 (Claude Code)", "construction": "Periodic bivariate-bicycle code on Z_31 x Z_6 (n = 2*l*m = 372): x = S_31 tensor I_6, y = I_31 tensor S_6 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^10y^3 + x^13y^3 + x^22y^0, B = x^0y^0 + x^2y^0 + x^5y^4 + x^16y^2; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(31, 6, [[0, 0], [10, 3], [13, 3], [22, 0]], [[0, 0], [2, 0], [5, 4], [16, 2]])). gcd(31, 6) = 1, so Z_31 x Z_6 is cyclic of order 186 and the code is the cyclic generalized-bicycle code over Z_186 with a(z) = z^0 + z^75 + z^84 + z^165, b(z) = z^0 + z^126 + z^140 + z^160 (CRT relabeling x^a y^b -> z^t, t = a mod 31, t = b mod 6).", "date": "2026-09-27" } }