Decoder Dependence in Surface-Code Threshold Estimation with Native Gottesman-Kitaev-Preskill Digitization and Parallelized Sampling

We quantify decoder dependence in surface-code threshold studies under two matched regimes: Pauli noise and native GKP-style Gaussian displacement digitization. Using LiDMaS+ v1.1.0, we benchmark MWPM, Union-Find (UF), Belief Propagation (BP), and neural-guided MWPM with fixed seeds, identical sweep grids, and unified reporting across runs 06--14. At d=5 and σ=0.20, MWPM and UF define the Pareto frontier, with (runtime, LER) = (1.341 s, 0.2273) and (1.332 s, 0.2303); neural-guided MWPM is slower and less accurate (1.396 s, 0.3730), and BP is dominated (7.640 s, 0.6107). Crossing-bootstrap diagnostics are stable only for MWPM, with median σ^star_3,5=0.10 (1911/2000 valid) and σ^star_5,7=0.1375 (1941/2000 valid), while other decoders show no valid crossing samples. Dense-window scanning over σin [0.08,0.24] returns NaN crossings for all decoders, confirming estimator- and window-sensitive threshold localization. Rank-stability and effect-size bootstrap analyses reinforce ordering robustness: BP remains rank 4, neural-guided MWPM rank 3, and MWPM-UF differences are small $Δ_MWPM-UF=-0.00383$, 95\% interval $[-0.0104,0.00329]$ across σin [0.05,0.35]. Threaded execution preserves statistical fidelity while improving throughput: 1.34times speedup in Pauli mode and 1.94times in native GKP mode, with mean |ΔLER| 6.07times10^-3 and 5.20times10^-3, respectively. We therefore recommend estimator-conditional threshold reporting coupled to runtime-fidelity checks for reproducible hardware-facing practical future decoder benchmarking workflows.