  As the signature manifestation of QCD in high energy nuclear collisions jet
production provides essential tests of that theory. But event-wise jet
reconstruction can be complex and susceptible to measurement bias. And QCD
theory in the form of Monte Carlo models of elementary collisions can also be
complex and difficult to test. It may be beneficial to construct a simple
static model of jet production in p-p collisions to facilitate data comparisons
and model tests. QCD is a logarithmic theory featuring variations with energy
scale of the form $\log(s/s_0)$. Jet-related data such as parton fragmentation
functions plotted on logarithmic rapidities exhibit self-similar scaling
behavior which admits simple and accurate parametrization with only a few
parameters. In this study we extend that method to construct a parametrization
of jet (scattered parton) momentum spectra based on certain measured
logarithmic jet production trends. The parametrization is established with
Sp\=pS jet data and then extrapolated for comparison with Tevatron and LHC jet
data. In addition, the jet production model from the present study is combined
with a parametrization of p-\=p fragmentation functions to predict the
minimum-bias jet fragment contribution to hadron $p_t$ spectra. The prediction
is compared with published p-p spectrum data to test the self-consistency of
the model.
