Output of the line finding done on the simulated ALMA observation that had an off-centered line and continuum source, which was initialized to have an integrated S/N of 5 in the integrated velocity map (see Fig. 4). In blue, we show the underlying PDF of a false detection ${\mathcal{P}}_{\mathrm{F}\mathrm{D}}(x)$ derived from counting peak values in the jackknifed realizations. In orange, we show the results on the simulated data, which shows a clear detection of the two sources at a S/N = 5. The peak at S/N ≈ 3.6 is consistent with being noise (as explained in the main body of the text).