  Following our previous work, we conclude that a GRB standard candle
constructed from the Ghirlanda et al. power-law relation between the
geometry-corrected energy (E_gamma) and the peak of the rest-frame prompt burst
spectrum (E_p) is not yet cosmographically useful, despite holding some
potential advantages over SNe Ia. This is due largely to the small sample of
\~20 GRBs with the required measured redshifts, jet-breaks, and peak energies,
and to the strong sensitivity of the goodness-of-fit of the power-law to input
assumptions. The most important such finding concerns the sensitivity to the
generally unknown density (and density profile), of the circumburst medium.
Although the E_p-E_gamma relation is a highly significant correlation over many
cosmologies, until the sample expands to include many low-z events, it will be
most sensitive to Omega_M but essentially insensitive to Omega_Lambda and w,
with some hope of constraining dw/dt with high-z GRB data alone. The relation
clearly represents a significant improvement in the search for an empirical GRB
standard candle, but is further hindered by an unknown physical basis for the
relation, the lack of a low-z training set to calibrate the relation in a
cosmology-independent way, and several major potential systematic uncertainties
and selection effects. Until these concerns are addressed, a larger sample is
acquired, and attempts are made to marginalize or perform Monte Carlo
simulations over the unknown density distribution, we urge caution concerning
claims of the utility of GRBs for cosmography and especially the attempts to
combine GRBs with SNe Ia.
