In string theory and in topological quantum field theory one encounters operators whose effect in correlation functions is simply to measure the topology of 2d spacetime. In particular these 'dilation'-type operators count the number of other operators via contact terms with the latter. While contact terms in general have a reputation for being convention-dependent, the ones considered here are perfectly well-defined by virtue of their simple geometrical meaning: They reflect the geometry of the stable-curve compactification. We give an unambiguous prescription for their evaluation which involves no analytic continuation in momenta.