  We introduce a framework for studying the effects of self-interaction on the
construction of point particle initial data in General Relativity. Within this
framework we rigorously prove the vanishing mass claim made by Arnowitt, Deser
and Misner regarding point sources. We identify a geometric structure and a
scaling parameter that allow one to determine, by controlling the effects of
self-interaction, when one does or does not obtain a non-zero mass.
