  We show that the Platinum gamma-ray burst (GRB) data compilation, probing the
redshift range $0.553 \leq z \leq 5.0$, obeys a cosmological-model-independent
three-parameter fundamental plane (Dainotti) correlation and so is
standardizable. While they probe the largely unexplored $z \sim 2.3-5$ part of
cosmological redshift space, the GRB cosmological parameter constraints are
consistent with, but less precise than, those from a combination of baryon
acoustic oscillation (BAO) and Hubble parameter [$H(z)$] data. In order to
increase the precision of GRB-only cosmological constraints, we exclude common
GRBs from the larger Amati-correlated A118 data set composed of 118 GRBs and
jointly analyze the remaining 101 Amati-correlated GRBs with the 50 Platinum
GRBs. This joint 151 GRB data set probes the largely unexplored $z \sim
2.3-8.2$ region; the resulting GRB-only cosmological constraints are more
restrictive, and consistent with, but less precise than, those from $H(z)$ +
BAO data.
