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Editing a double-precision coverage, in ArcMap, may increase the size of the verified fuzzy tolerance. The fuzzy tolerance of single-precision coverages is not affected.
Two conversions are performed to allow coverages to be edited in ArcMap.
A coverage must be converted into integer space for the Geodatabase framework to handle it during an edit session. This conversion reduces the precision from 14 to 9 significant digits. This is where most of the precision is lost.
A second conversion must be done to work inside the usable coordinate range of the Topology Engine.
CLEAN or BUILD is run after saving the edits in ArcMap, unless only attribute edits were made. CLEAN uses the larger of the existing fuzzy tolerance and the tolerance calculated by the Topology Engine. Once the CLEAN operation completes, the fuzzy tolerance is set to this value.
This is a known limitation. In most cases the loss in precision does not have an adverse effect on the accuracy of the data.