  In this paper we develop a projective phase space generator appropriate for
hadron collider geometry. The generator integrates over bremsstrahlung events
which project back to a single, fixed Born event. The projection is dictated by
the experimental jet algorithm allowing for the forward branching phase space
generator to integrate out the jet masses and initial state radiation. When
integrating over the virtual and bremsstrahlung amplitudes this results in a
single K-factor, assigning an event probability to each Born event. This
K-factor is calculable as a perturbative expansion in the strong coupling
constant. One can build observables from the Born kinematics, giving identical
results to tradi- tional observables as long as the observable does not depend
on the infrared sensitive jet mass or initial state radiation.
