Nearest-neighbour comparisons for N = 200 points drawn from a uniform spherical distribution within R = 1.0. Top: NN graph constructed in 3D, where the blue connections are the 3D NNs (left); 2D projection, where the orange connections are the 2D NNs (Centre); and the corresponding distributions of NN edge lengths (right) highlighting the overall shortening in projection. Bottom: detailed breakdown. The left panel repeats the 2D overlay of 3D and 2D edges, while the right panels show the distributions of ℓ_3D, ℓ_2D for shared edges and the ratios ℓ_3D/ℓ_2D. Vertical dashed lines mark the medians, and KDEs are overplotted on the histograms. Together these panels illustrate how projection both compresses lengths and reassigns neighbours, with only the very shortest pairs surviving unchanged.