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71, 123, 126, 138, 143, 146, 158, 211, 231, 283, 286, 298, 303, 306, 318, 331, 351, 379, 399, 401, 414, 421, 434, 481, 501, 529, 549, 564, 571, 584, 591 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 1200000, "tool": "verify/gf2_fast distance_rand_witness (laptop, 3 x 400,000 trials)", "seeds": [ 100, 101, 102 ], "survived_samples": 50000000 } }, "d": 32 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group-algebra code (Lin and Pryadko, arXiv:2306.16400) on G = C8:C40(r=7) of order 320, Cayley table research/kit/group_algebra.metacyclic(8, 40, 7) 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, 13, 18, 275], b = [0, 52, 125, 302] (element indices). n = 2|G| = 640, 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 0 failures, X memory 3 failures, against 20 copies of the distance-7 rotated surface code (1940 physical qubits, same builder and decoder) with 116 and 102 failures. Decoder-based d_circ estimate at 3 rounds: 52. 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" } }