Illustration of our “hot and cold” detection technique. Left: a 90″ × 90″ cutout of the COSMOS-Web ${\chi }_{+}^2$ detection image, showing Kron ellipses of all detected sources found from cold mode (blue) and hot mode (orange) SEP runs. Note the star in the lower-right corner that has been manually masked. Right: catalog completeness and contamination measured using an independent catalog from PRIMER (which reaches one magnitude deeper). Completeness is measured as a fraction of PRIMER sources recovered as a function of F277W magnitude (the deepest COSMOS-Web filter) for cold-mode (blue) and hot-mode (orange) sources. Contaminants are measured as sources found in COSMOS-Web but not detected in PRIMER imaging. We split these measurements into “2 exposure” (bottom row) and “4 exposure” (top row) areas where the imaging depth varies significantly. Completeness at the 8σ (5σ) survey depth exceeds 95% (80%) and contamination at these depths does not exceed 2% (4%).