We report measurements of transverse momentum p(t) spectra for ten event multiplicity classes of p-p collisions at root s=200 GeV. By analyzing the multiplicity dependence we find that the spectrum shape can be decomposed into a part with amplitude proportional to multiplicity and described by a Levy distribution on transverse mass m(t), and a part with amplitude proportional to multiplicity squared and described by a Gaussian distribution on transverse rapidity y(t). The functional forms of the two parts are nearly independent of event multiplicity. The two parts can be identified with the soft and hard components of a two-component model of p-p collisions. This analysis then provides the first isolation of the hard component of the p(t) spectrum as a distribution of simple form on y(t).
