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427, 430, 436, 529 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 20000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1928504117, 755471799 ], "survived_samples": 999999996 } }, "Z": { "value": 28, "confidence": "upper_bound", "witness": [ 44, 47, 50, 59, 62, 68, 71, 74, 89, 182, 188, 191, 194, 267, 269, 286, 288, 290, 307, 309, 328, 347, 368, 410, 431, 450, 513, 515 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 166666666, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 755471799, 755471800, 755471801, 755471802, 755471803, 755471804 ], "survived_samples": 999999996 } }, "d": 28 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code over Z_267 (n = 2m = 534): a(x) = 1 + x^129 + x^249 + x^264, b(x) = 1 + x^164 + x^183 + x^246; H_X = [circ(a)|circ(b)], H_Z = [circ(b)^T|circ(a)^T], where circ(v) has first row v and row i = v rolled by i (research/cyclic_gb.py build_cyclic_gb(267, a, b) with a, b the 0/1 first rows). k = 2 deg gcd(a, b, x^267 + 1).", "date": "2026-09-26", "notes": "Found by the fourth LER-objective search (cyclic generalized-bicycle codes with check weight 6, 7, or 8 at 420 < n <= 700 and k >= 8): circuit-level logical error rate at 3 rounds under the board's depolarizing recipe, interleaved schedule, decoded with CUDA-Q QEC nv-qldpc-decoder (BP+OSD-CS order 10). At p = 0.002, 100000 shots per basis: Z memory 16 failures, X memory 16 failures, against 24 copies of the distance-5 rotated surface code (1176 physical qubits, same builder and decoder) with 1095 and 1116 failures. Decoder-based d_circ estimate at 3 rounds: 34. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. A norm-lift quotient bound over the divisors of m and a single-block kernel bound were run before admission (lightest lift 39). Details in the accompanying note.", "model": "Claude Fable 5.1 (Claude Code)", "origin": "submission", "novelty": "unknown" } }