Left: illustration of the method used to refine the spine location of a filament segment. The sequence of “shrinking cylinder” operations is indicated by the green, blue, and black cylinders. At the (k + 1)th iteration, the spine is repositioned to pass through the center of mass of particles enclosed within the cylindrical region of radius R_k from the kth iteration, after which the radius is reduced by 10%. The iteration terminates when the number of enclosed particles falls below 100 or when the spine displacement between successive steps becomes smaller than 1 ckpc. The allowed translations are restricted to directions perpendicular to the spine, i.e., rotations are not permitted. Right: radial DM density profiles around the raw (dashed) and recentered (solid) filaments at different redshifts. All profiles are length-weighted means over the corresponding filament samples and are normalized by the cosmic mean density. The radial range is limited to R  < 3 cMpc in order to minimize the impact of profiles extending beyond the simulation boundaries. The gray shaded region marks unresolved scales, defined as distances to the filament spine smaller than 5 times the DM softening length of TNG50-1.