Distribution of separations between dense cores and the nearest filament crests in the DisPerSE raw sample of filaments. The green histogram is for all 1768 starless cores, the light blue histogram for the 804 candidate prestellar cores, and the dark blue histogram for the 490 robust prestellar cores. The vertical lines mark the half widths (i.e., on either side of the filament crests) of a 0.1 pc-wide (red), 0.5 × 0.1 pc-wide (inner black), and a 2 × 0.1 pc-wide (outer black) filament.