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"verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 174710593, 174710594, 174710595, 174710596, 174710597, 174710598 ], "survived_samples": 300000000 } }, "Z": { "value": 43, "confidence": "upper_bound", "witness": [ 5, 18, 24, 27, 36, 57, 62, 66, 71, 75, 80, 93, 96, 105, 123, 126, 135, 138, 141, 171, 186, 192, 216, 243, 247, 252, 261, 273, 277, 291, 300, 304, 306, 325, 353, 375, 397, 411, 463, 502, 548, 559, 578 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 174710593, 174710594, 174710595, 174710596, 174710597, 174710598 ], "survived_samples": 300000000 } }, "d": 43 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Periodic bivariate-bicycle code on Z_31 x Z_10 (n = 2*l*m = 620): x = S_31 tensor I_10, y = I_31 tensor S_10 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^5y^8 + x^6y^7 + x^15y^7, B = x^0y^0 + x^14y^8 + x^18y^4 + x^20y^6; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(31, 10, [[0, 0], [5, 8], [6, 7], [15, 7]], [[0, 0], [14, 8], [18, 4], [20, 6]])). gcd(31, 10) = 1, so Z_31 x Z_10 is cyclic of order 310 and the code is the cyclic generalized-bicycle code over Z_310 with a(z) = z^0 + z^37 + z^77 + z^98, b(z) = z^0 + z^138 + z^204 + z^206 (CRT relabeling x^a y^b -> z^t, t = a mod 31, t = b mod 10).", "date": "2026-09-26", "notes": "Found by the fourth LER-objective search (coprime bivariate-bicycle codes (gcd(l, m) = 1) 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 6 failures, against 14 copies of the distance-7 rotated surface code (1358 physical qubits, same builder and decoder) with 96 and 93 failures. Decoder-based d_circ estimate at 3 rounds: 76. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. A norm-lift quotient bound over the divisors of m and a single-block kernel bound were run before admission (lightest lift 60). Details in the accompanying note.", "model": "Claude Fable 5.1 (Claude Code)", "origin": "submission", "novelty": "unknown" } }