Cosmological Constraints from Bias-Robust Wavelet Scattering Statistics for Stage-IV Galaxy Surveys

A central challenge in precision cosmology with galaxy surveys is to extract non-Gaussian information from large-scale structure while controlling systematic uncertainties such as tracer bias. Conventional clustering statistics, such as the two-point correlation function (2PCF), capture limited nonlinear information and typically require explicit bias modeling, which can introduce systematic errors if the adopted bias prescription is inaccurate. To address this problem, we introduce $R^{\rm wst}$, a bias-robust statistic constructed from $m$-mode ratios of the wavelet scattering transform (WST). Using simulation-based inference, we train a Gaussian-process-regression emulator on the \texttt{Kun} simulation suite and use \texttt{JiuTian} simulations for covariance estimation and validation. The emulator achieves percent-level accuracy, sufficient for the expected observational uncertainties. We show that $R^{\rm wst}$ yields unbiased constraints on $\Omega_m$, $\sigma_8$, $n_s$, and $w_0$, and improves the breaking of the $\Omega_m$--$\sigma_8$ degeneracy by about a factor of two compared with 2PCF. Its constraining power remains stable across a broad range of tracer-bias scenarios, demonstrating that $R^{\rm wst}$ can mitigate bias-induced systematics without explicit bias modeling. These results establish $R^{\rm wst}$ as a powerful and robust statistic for precision cosmology with Stage-IV surveys.