  The use of GRB energetics for cosmography has long been advanced as a means
to probe out to high redshifts, to the epoch of deceleration. However, the
prompt energy release in GRBs, even when corrected for jetting geometry, is far
from being a standard candle. We explore the cosmographic potential of a GRB
standard candle based on the newly-discovered relation by Ghirlanda et al.
between the apparent geometry-corrected energies (E_gamma) and the peak of the
prompt burst spectrum (E_p). We present an explicit, self-consistent formalism
for correcting GRB energies with a thorough accounting for observational
uncertainties. In contrast to other work, we demonstrate that the current
sample of 19 GRBs is not yet cosmographically competitive with results from
other studies (e.g., SNe Ia). Although the E_p-E_gamma relation is a
significant correlation across a range of cosmologies, the goodness of fit of
the data to a power law, depends strongly on input assumptions -- especially
the unknown density of the circumburst medium. Independent of assumptions, with
very few low-z bursts, the current sample is most sensitive to Omega_M but
essentially insensitive to Omega_Lambda. The proper use of the relation clearly
brings GRBs an impressive step closer toward a standardizable candle, but until
the physical origin of the E_p-E_gamma relation is understood, calibrated with
a training set of low redshift bursts, and the major potential systematic
uncertainties and selection effects are addressed, we urge caution concerning
claims of the utility of GRBs for cosmography (abridged).
