Robustness of cosmic void statistics: insights from SDSS DR7 and the ELUCID simulation

We present a systematic analysis of the statistical properties of cosmic voids using galaxies from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and subhaloes from the ELUCID constrained simulation. By comparing voids identified in redshift space, real space, and reconstructed volumes, we assess the impact of redshift-space distortions (RSD) and tracer bias. Using the \texttt{VAST} toolkit, we apply both the geometry-based \texttt{VoidFinder} algorithm and watershed-based methods. We find that void properties are not equally robust. The three-dimensional morphology of voids, quantified by their sphericity and triaxiality, remains stable across different reconstructions and tracer selections. In contrast, void size distributions and radial density profiles depend strongly on the identification algorithm, with watershed-based methods systematically producing larger voids and higher compensation walls than \texttt{VoidFinder}. Using the full ELUCID simulation box, we show that tracer bias mainly affects void density profiles, with noticeable changes only for the most massive subhaloes ($>10^{11.5}\,h^{-1}{\rm M}_\odot$). The agreement between SDSS observations, the ELUCID reconstruction, and the full simulation box demonstrates the high fidelity of constrained simulations and reveals a clear hierarchy in the robustness of void statistics.