Gigaparsec structures are nowhere to be seen in $\Lambda$CDM: an enhanced analysis of LSS in FLAMINGO-10K simulations

Recently, Sawala et al. 2025 claimed to refute the cosmological significance of the Giant Arc based on their analysis of the FLAMINGO-10K simulation data. In our paper here, we highlight several shortcomings of the authors' analysis. We then perform an enhanced analysis on the FLAMINGO-10K simulation data with applications of: the Single-Linkage Hierarchical Clustering (SLHC), the Convex Hull of Member Spheres (CHMS), and the Minimal Spanning Tree (MST) algorithms. Using the full $2.8^3$ Gpc$^3$ FLAMINGO-10K box, with subhaloes at $z=0.7$, and $100$ random realisations (from random subset selections) we find no gigaparsec structures in FLAMINGO-10K, and only a few ultra-large large-scale structures (uLSSs, structures exceeding a maximum pairwise separation of $370$ Mpc). Somewhat surprisingly, we found that the large-scale aspects of the FLAMINGO-10K data could be adequately represented by a Poisson point distribution. The enhanced analysis presented here further supports the remarkable nature of the Giant Arc as a cosmologically-significant structure. Of course, the Giant Arc is also accompanied by a second uLSS, the Big Ring. The analysis presented here builds on the work presented by Sawala et al., but amends the application of their statistical assessments. We do not yet know why there appears to be such a large discrepancy between the FLAMINGO-10K data and the observed LSS in MgII absorbers. Perhaps the results presented here might suggest that the GA, and especially the GA + BR, presents a more direct challenge to $\Lambda$CDM. In contrast to the conclusion of Sawala et al. that `gigaparsec patterns abound in a $\Lambda$CDM universe' we find that they are nowhere to be seen.