Catalog detection efficiency as a function of apparent magnitude, derived from implanted fake objects in the data. Fakes are assigned neutral colors (g − r = r − i = i − z = 0), such that the detection efficiency is treated as magnitude-dependent only. Each data point represents the recovery fraction of implanted fakes in a given magnitude bin. Curves show maximum-likelihood fits to the logistic function in Equation (5), where η₀ is the plateau efficiency, m₅₀ is the 50% completeness magnitude, and σ controls the transition width. Fits are performed independently for each observing season, yielding η₀ = 0.74, m₅₀ = 23.87, σ = 0.38 for 2015 and η₀ = 0.75, m₅₀ = 23.77, σ = 0.40 for 2016. These fitted parameters are used in the nondetection test to evaluate whether candidate links have plausible detection rates given their apparent brightness and survey coverage.