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305, 321, 322, 327, 328 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-27", "found_at_samples": 300000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 897722913 ], "survived_samples": 300000000 } }, "Z": { "value": 27, "confidence": "upper_bound", "witness": [ 2, 23, 24, 30, 42, 45, 56, 68, 94, 95, 113, 114, 115, 116, 124, 126, 141, 147, 157, 170, 177, 191, 217, 267, 274, 295, 301 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-27", "found_at_samples": 300000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 897722913 ], "survived_samples": 300000000 } } }, "provenance": { "authors": [ "@vprusso" ], "model": "Claude Fable 5.1 (Claude Code)", "construction": "Periodic bivariate-bicycle code on Z_33 x Z_5 (n = 2*l*m = 330): x = S_33 tensor I_5, y = I_33 tensor S_5 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^11y^3 + x^16y^4 + x^31y^0, B = x^0y^0 + x^1y^2 + x^29y^4 + x^31y^4; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(33, 5, [[0, 0], [11, 3], [16, 4], [31, 0]], [[0, 0], [1, 2], [29, 4], [31, 4]])). gcd(33, 5) = 1, so Z_33 x Z_5 is cyclic of order 165 and the code is the cyclic generalized-bicycle code over Z_165 with a(z) = z^0 + z^49 + z^130 + z^143, b(z) = z^0 + z^29 + z^64 + z^67 (CRT relabeling x^a y^b -> z^t, t = a mod 33, t = b mod 5).", "date": "2026-09-27" } }