  Nuclear modification factors (NMFs) are spectrum ratios rescaled by an
estimate of the number of binary N-N collisions $N_{bin}$ within an A-B
collision. NMFs from more-central A-A collisions have been interpreted to
indicate formation of a quark-gluon plasma (QGP) when compared with results
from control $p$-A or $d$-A collisions. However, subsequent analyses of such
control systems are now also interpreted to indicate QGP formation, calling
into question proper interpretation of NMFs. An additional complication is the
nature of the so-called ``Cronin effect'' contribution to NMF structure that is
not well understood. In the present study a two-component model of hadron
production (TCM) is applied to identified-hadron (PID) $p_t$ spectra from 5 GeV
$p$-Pb collisions extending up to 20 GeV/c. Hard components (jet fragment
distributions) are accurately isolated and their evolution with collision
centrality parametrized. The TCM is then applied to NMFs without rescaling by
$N_{bin}$, allowing direct comparisons between NMF evolution and hard-component
evolution with centrality. To address the Cronin effect the TCM is applied to
fixed-target $p$-A spectra from the Chicago-Princeton (C-P) collaboration, the
origin of the Cronin effect. Inferred C-P spectrum hard components are
quantitatively consistent with extrapolation of jet-related structure from
higher energies. As a general conclusion spectrum ratios such as NMFs are
difficult to interpret, whereas direct differential analysis of isolated
spectra may be interpreted simply and accurately.
