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30, 31, 32, 33, 34, 35, 84, 86, 88, 90, 92, 94, 168, 170, 172, 174, 176, 178, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 252, 254, 256, 258, 260, 262 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 746282076, 746282077, 746282078, 746282079, 746282080, 746282081 ], "survived_samples": 300000000 } }, "Z": { "value": 60, "confidence": "upper_bound", "witness": [ 0, 6, 7, 11, 18, 19, 30, 31, 33, 35, 36, 45, 47, 59, 68, 71, 74, 92, 97, 110, 116, 121, 128, 132, 133, 139, 168, 169, 173, 174, 180, 181, 192, 193, 195, 197, 207, 209, 210, 221, 230, 233, 248, 254, 271, 278, 284, 290, 295, 301, 306, 307, 336, 436, 443, 445, 510, 605, 610, 619 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 746282076, 746282077, 746282078, 746282079, 746282080, 746282081 ], "survived_samples": 300000000 } }, "d": 48 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group-algebra code (Lin and Pryadko, arXiv:2306.16400) on G = C28:C12(r=15) of order 336, Cayley table research/kit/group_algebra.metacyclic(28, 12, 15) 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, 71, 77, 209], b = [0, 33, 119, 175] (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 2 failures, X memory 2 failures, against 16 copies of the distance-7 rotated surface code (1552 physical qubits, same builder and decoder) with 66 and 58 failures. Decoder-based d_circ estimate at 3 rounds: 48. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. A second, independent pass at 999,999,996 trials per side, with its own seeds, returned the same minimum weight, so two randomized searches of different budgets agree on the bound; the stored receipt is the 300,000,000-trial pass. Details in the accompanying note.", "model": "Claude Fable 5.1 (Claude Code)", "origin": "submission", "novelty": "unknown" } }