  Using a simple geometric framework with a realistic nuclear density
distribution, we fit published HERMES data to determine fundamental properties
of hadronization using the nuclear medium as a spatial analyzer. Our approach
uses a fit to the transverse momentum broadening observable and the hadronic
multiplicity ratio; the simultaneous fit to two different observables strongly
constrains the outcome. Using the known sizes of the target nuclei, we extract
the color lifetime, finding a z$\mathrm{_h}$-dependent range of values from 2
to 8 fm/c for these data. We also extract estimates for the $\hat{q}$ transport
coefficient characterizing the strength of the interaction between the quark
and the cold nuclear medium, finding an average value of 0.035$\pm$0.011
GeV$\mathrm{^2}$/fm. With a three-parameter model we obtain satisfactory fits
to the data with a goodness-of-fit parameter $\chi ^2$/dof of 1.1 or less. In a
secondary fit of the results from that model we independently find a value for
the Lund String Model string tension of 1.00$\pm$0.05 GeV/fm. We evaluated the
sensitivity for extracting quark energy loss and effective in-medium hadronic
cross sections using four-parameter variants of the model, finding large
uncertainties in both cases. Our results suggest that hadronic interaction of
forming hadrons in the nuclear medium is the primary dynamical cause of meson
attenuation in the HERMES data, with quark energy loss playing a more minor
role.
