Illustration of the impact of a finite SDR on NN statistics using a uniform distribution of N = 200 points within a sphere of radius R = 1.0. Left: intrinsic 3D NN graph. Centre: two-dimensional projection after applying a beam–blending step that merges points closer than one beam width, corresponding here to a SDR of SDR = FoV/FWHM_beam = 10. Circles mark the original 2D positions (open) and the resulting beam-blended centroids (filled). Right: distributions of NN edge lengths in 3D and 2D after blending. In this example, 135 of the 200 projected cores (67.5%) are merged into 65 effective groups, erasing all topological correspondence between the intrinsic and projected networks (J = 0.00, overlap fraction = 0). The typical 3D and 2D NN lengths become nearly equal (⟨ℓ_3D⟩/⟨ℓ_2D⟩ ≃ 1.0), as beam blending suppresses the shortest intrinsic separations that normally produce the geometric compression factor (4/π ≃ 1.27). This example illustrates that limited spatial resolution can strongly distort the apparent connectivity and scale distribution of dense cores even in an intrinsically uniform configuration.