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8, 31, 39, 62, 70, 93, 101, 124, 132, 155, 163, 207, 212, 238, 243, 269, 274, 300, 305, 331, 336, 362, 367 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1792469568, 1359114882 ] } }, "Z": { "value": 24, "confidence": "upper_bound", "witness": [ 3, 29, 34, 60, 65, 91, 96, 122, 127, 153, 158, 184, 202, 210, 233, 241, 264, 272, 295, 303, 326, 334, 357, 365 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1792469568, 1359114882 ] } }, "d": 24 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code over Z_186 (n = 2m = 372): a(x) = 1 + x^59 + x^88, b(x) = 1 + x^23 + x^80 + x^132; 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(186, a, b) with a, b the 0/1 first rows). k = 2 deg gcd(a, b, x^186 + 1).", "date": "2026-09-24", "model": "Claude Fable 5.1 (Claude Code)", "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, 60,000 shots per basis: Z memory 13 failures, X memory 10 failures, against 14 copies of the distance-7 rotated surface code (1358 physical qubits, same builder and decoder) with 145 and 173 failures. Decoder-based d_circ estimate at 3 rounds: 72. 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" } }