Left: distribution of Gaia DR3 sources densities computed in 196,608 HEALPix regions level 7 across the whole sky. Crowding artificially sets an upper limit of the catalogue source density. Right: source density as a function of M₁₀ in Gaia DR3 (black) and DECaPS with r<23 (cyan) in the 2906 patches we use to calibrate our model (see Fig. C.1). Outside the sparsest regions, the Gaia source density provides almost no information on the true source density and level of crowding.