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NVIDIA A40)", "seeds": [ 588050700, 1593625337 ], "survived_samples": 50000000 } }, "Z": { "value": 22, "confidence": "upper_bound", "witness": [ 0, 2, 4, 19, 21, 53, 73, 86, 105, 115, 121, 122, 137, 142, 155, 157, 170, 270, 297, 303, 322, 334 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 588050700, 1593625337 ] } }, "d": 22 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code over Z_170 (n = 2m = 340): a(x) = 1 + x^15 + x^84, b(x) = 1 + x^12 + x^133 + x^164; 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(170, a, b) with a, b the 0/1 first rows). k = 2 deg gcd(a, b, x^170 + 1).", "date": "2026-09-25", "notes": "Found by the third LER-objective search (weight-6 and weight-7 two-block codes at 300 < n <= 420 with k >= 12): 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 24 failures, X memory 38 failures, against 16 copies of the distance-5 rotated surface code (784 physical qubits, same builder and decoder) with 1569 and 1716 failures. Decoder-based d_circ estimate at 3 rounds: 64. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. Details in the accompanying note.", "origin": "submission", "novelty": "unknown", "model": "Claude Fable 5.1 (Claude Code)" } }