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"witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-27", "found_at_samples": 300000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 110075763 ], "survived_samples": 300000000 } }, "Z": { "value": 26, "confidence": "upper_bound", "witness": [ 0, 6, 12, 24, 52, 86, 92, 105, 111, 117, 129, 157, 191, 197, 210, 216, 228, 234, 262, 274, 315, 321, 333, 339, 367, 379 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-27", "found_at_samples": 300000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 110075763 ], "survived_samples": 300000000 } } }, "provenance": { "authors": [ "@vprusso" ], "model": "Claude Fable 5.1 (Claude Code)", "construction": "Periodic bivariate-bicycle code on Z_70 x Z_3 (n = 2*l*m = 420): x = S_70 tensor I_3, y = I_70 tensor S_3 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^1y^1 + x^23y^0 + x^32y^1, B = x^0y^0 + x^7y^1 + x^45y^2 + x^66y^0; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(70, 3, [[0, 0], [1, 1], [23, 0], [32, 1]], [[0, 0], [7, 1], [45, 2], [66, 0]])). gcd(70, 3) = 1, so Z_70 x Z_3 is cyclic of order 210 and the code is the cyclic generalized-bicycle code over Z_210 with a(z) = z^0 + z^1 + z^93 + z^172, b(z) = z^0 + z^7 + z^66 + z^185 (CRT relabeling x^a y^b -> z^t, t = a mod 70, t = b mod 3).", "date": "2026-09-27" } }