Effects of galaxy catalog incompleteness within the CHIMERA framework. (a) Sky localization and pixelization (represented with the grid) for a GW event from a stellar mass-weighted MICECATv2 catalog (the underlying blue points). The marker shows the host true position and pixel, from which the distributions in the subsequent panel are computed. (b) Catalog redshift distribution for complete (light blue), i < 22 cut (blue), and empty catalogs (dark blue flat line). The arrow shows the true host redshift. (c) Completion terms accounting for missing galaxies; dark blue shows the background distribution used in standard siren constraints. (d) Resulting galaxy distribution terms, individually normalized for better comparison.