For once, the variation of girdle thinckness could say things about the precision of the cut and the variations in thickness produced in a stone with fine 3D symmetry by the alignment of facets.
However, it would be very unusual (If I knew more diamonds by birthmarks I would dare say impossible) to get a range of more than one 'step' (say, "thin - slghtly thick") on a GIA cert of a H&A stone - with differences of less than 1% expected between the min and max for stones around 1ct.
But some variation is inbuilt in the design of the RBC cut - and the example below shows what a nicely executed girdle would look like.
The variation of thickness could get wider than the range below, and, as long as the pattern of thin - thick - thin portions remains symmetrycal there is little else worth a word. Actually, some rounds owe their 'edge to edge' brilliance to a certain placement of the facets that does produce such variation (but nothing extreme) on the girdle as a side effect.
btw: all images come from somewhere on the GoodOldGold site
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