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40, 42, 44, 46, 48, 50, 52, 54, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 196, 198, 200, 202, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 281, 283, 285, 287, 289, 291, 293, 295, 297, 299, 301, 303, 305, 307 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1605195543, 1605195544, 1605195545, 1605195546, 1605195547, 1605195548 ], "survived_samples": 300000000 } }, "Z": { "value": 84, "confidence": "upper_bound", "witness": [ 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 260, 264, 268, 272, 276, 280, 284, 288, 292, 296, 300, 304, 308, 312, 316, 320, 324, 328, 332 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1605195543, 1605195544, 1605195545, 1605195546, 1605195547, 1605195548 ], "survived_samples": 300000000 } }, "d": 56 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group-algebra code (Lin and Pryadko, arXiv:2306.16400) on G = C12:C28(r=11) of order 336, Cayley table research/kit/group_algebra.metacyclic(12, 28, 11) with the identity at index 0 and elements indexed as that builder lists them: H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] with L(g)[g h, h] = 1 and R(g)[h g, h] = 1 (research/kit/group_algebra.py build_2bga(mul, a, b)); a = [0, 183, 208, 303], b = [0, 89, 225, 310] (element indices). n = 2|G| = 672, check weight 8.", "date": "2026-09-26", "notes": "Found by the fourth LER-objective search (two-block group-algebra codes over non-abelian groups 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 1 failures, X memory 0 failures, against 14 copies of the distance-7 rotated surface code (1358 physical qubits, same builder and decoder) with 43 and 58 failures. Decoder-based d_circ estimate at 3 rounds: 56. 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.", "model": "Claude Fable 5.1 (Claude Code)", "origin": "submission", "novelty": "unknown" } }