  As a result of spherical kinematics, temporal evolution of received gamma-ray
emission should demonstrate signatures of curvature from the emitting shell.
Specifically, the shape of the pulse decay must bear a strict dependence on the
degree of curvature of the gamma-ray emitting surface. We compare the spectral
evolution of the decay of individual GRB pulses to the evolution as expected
from curvature. In particular, we examine the relationship between photon flux
intensity (I) and the peak of the \nu F\nu distribution (E_{peak}) as predicted
by colliding shells. Kinematics necessitate that E_{peak} demonstrate a
power-law relationship with I described roughly as: I=E_{peak}^{(1-\zeta)}
where \zeta represents a weighted average of the low and high energy spectral
indices. Data analyses of 24 BATSE gamma-ray burst pulses provide evidence that
there exists a robust relationship between E_{peak} and I in the decay phase.
Simulation results, however, show that a sizable fraction of observed pulses
evolve faster than kinematics allow. Regardless of kinematic parameters, we
found that the existence of curvature demands that the I - E_{peak} function
decay be defined by \sim (1-\zeta). Efforts were employed to break this
curvature dependency within simulations through a number of scenarios such as
anisotropic emission (jets) with angular dependencies, thickness values for the
colliding shells, and various cooling mechanisms. Of these, the only method
successful in dominating curvature effects was a slow cooling model. As a
result, GRB models must confront the fact that observed pulses do not evolve in
the manner which curvature demands.
