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"found_at_samples": 300000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1006530907 ], "survived_samples": 300000000 } }, "Z": { "value": 29, "confidence": "upper_bound", "witness": [ 7, 9, 23, 25, 39, 43, 56, 59, 70, 81, 92, 108, 125, 142, 148, 158, 164, 168, 170, 176, 221, 233, 252, 256, 272, 308, 314, 331, 332 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-27", "found_at_samples": 300000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1006530907 ], "survived_samples": 300000000 } } }, "provenance": { "authors": [ "@vprusso" ], "model": "Claude Fable 5.1 (Claude Code)", "construction": "Periodic bivariate-bicycle code on Z_25 x Z_7 (n = 2*l*m = 350): x = S_25 tensor I_7, y = I_25 tensor S_7 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^2y^2 + x^11y^3 + x^18y^4, B = x^0y^0 + x^2y^5 + x^14y^1 + x^14y^2; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(25, 7, [[0, 0], [2, 2], [11, 3], [18, 4]], [[0, 0], [2, 5], [14, 1], [14, 2]])). gcd(25, 7) = 1, so Z_25 x Z_7 is cyclic of order 175 and the code is the cyclic generalized-bicycle code over Z_175 with a(z) = z^0 + z^2 + z^18 + z^136, b(z) = z^0 + z^64 + z^114 + z^152 (CRT relabeling x^a y^b -> z^t, t = a mod 25, t = b mod 7).", "date": "2026-09-27" } }