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"survived_samples": 300000000 } }, "Z": { "value": 33, "confidence": "upper_bound", "witness": [ 17, 19, 20, 21, 64, 72, 112, 114, 119, 135, 143, 145, 146, 147, 150, 151, 152, 186, 199, 200, 205, 265, 287, 303, 310, 333, 334, 336, 348, 353, 370, 372, 384 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-27", "found_at_samples": 8000000, "tool": "verify/gate_changed.py RIS-fast (gf2_fast, structure-aware)", "survived_samples": 8000000 } } }, "provenance": { "authors": [ "@vprusso" ], "model": "Claude Fable 5.1 (Claude Code)", "construction": "Periodic bivariate-bicycle code on Z_49 x Z_4 (n = 2*l*m = 392): x = S_49 tensor I_4, y = I_49 tensor S_4 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^1y^3 + x^2y^0 + x^33y^0, B = x^0y^0 + x^8y^3 + x^13y^1 + x^46y^0; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(49, 4, [[0, 0], [1, 3], [2, 0], [33, 0]], [[0, 0], [8, 3], [13, 1], [46, 0]])). gcd(49, 4) = 1, so Z_49 x Z_4 is cyclic of order 196 and the code is the cyclic generalized-bicycle code over Z_196 with a(z) = z^0 + z^99 + z^100 + z^180, b(z) = z^0 + z^13 + z^144 + z^155 (CRT relabeling x^a y^b -> z^t, t = a mod 49, t = b mod 4).", "date": "2026-09-27" } }