Also known as "rounding up," the purpose of girdling is to create the edge that separates the crown and pavilion on a finished diamond. Whereas the thickness of the girdle controls durability (thin girdles are susceptible to chipping) – it is the roundness that ultimately controls symmetry.
For example, the pavilion mains on a round diamond with little or no variance in roundness can all be cut to the same depth into the girdle, at precisely the same angle, and come to a perfect point with the culet exactly in the center of the diamond. The same can be said of the bezel facets on the crown and the table being exactly centered.
This variance is calculated by the laboratories (GIA, AGS, IGI and EGL) by measuring the maximum and minimum diameters in millimeters with a variance of 1/10th mm deemed acceptable, e.g. 6.50 mm – 6.60 mm. Clearly these measurements cannot produce perfect symmetry as either the culet or the table (or both) would have to out of center to compensate for the lack of roundness. On the other hand, Hearts On Fire's use of proprietary girdling equipment produces results with variances of 3/100th mm resulting in near perfect symmetry.
Note: It is impossible to produce perfect roundness in earth’s atmosphere because of the effects of 14lbs per sq inch of gravity on the machinery...we’d have to produce diamonds in space to achieve perfect roundness.