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57, 62, 75, 80, 81, 90, 114, 119, 134, 145, 150, 168, 212, 228, 247, 262, 271, 277, 282, 290, 320, 322, 354, 365 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1351914191, 1005294220 ] } }, "Z": { "value": 26, "confidence": "upper_bound", "witness": [ 8, 10, 19, 27, 30, 49, 52, 59, 71, 83, 102, 124, 130, 146, 151, 175, 192, 233, 262, 268, 303, 305, 312, 322, 332, 345 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 1351914191, 1005294220 ] } }, "d": 26 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group-algebra code (Lin and Pryadko, arXiv:2306.16400) on G = C3:C62(r=2) of order 186, Cayley table research/kit/group_algebra.metacyclic(3, 62, 2) 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, 49, 92], b = [0, 77, 106, 116] (element indices). n = 2|G| = 372, check weight 7.", "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 3 failures, X memory 6 failures, against 12 copies of the distance-7 rotated surface code (1164 physical qubits, same builder and decoder) with 78 and 70 failures. Decoder-based d_circ estimate at 3 rounds: 69. 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)" } }