  Usually the boundary map in K-theory localization only gives the tame symbol
at $K_{2}$. It sees the tamely ramified part of the Hilbert symbol, but no wild
ramification. Gillet has shown how to prove Weil reciprocity using such
boundary maps. This implies Hilbert reciprocity for curves over finite fields.
However, phrasing Hilbert reciprocity for number fields in a similar way fails
because it crucially hinges on wild ramification effects. We resolve this
issue, except at p=2. Our idea is to pinch singularities near the ramification
locus. This fattens up K-theory and makes the wild symbol visible as a boundary
map.
