  The purpose of this note is to make several advances in the interpretation of
the balanced state sum model by Barrett and Crane in gr-qc/9709028 as a quantum
theory of gravity. First, we outline a shortcoming of the definition of the
model in pointed out to us by Barrett and Baez in private communication, and
explain how to correct it. Second, we show that the classical limit of our
state sum reproduces the Einstein-Hilbert lagrangian whenever the term in the
state sum to which it is applied has a geometrical interpretation. Next we
outline a program to demonstrate that the classical limit of the state sum is
in fact dominated by terms with geometrical meaning. This uses in an essential
way the alteration we have made to the model in order to fix the shortcoming
discussed in the first section. Finally, we make a brief discussion of the
Minkowski signature version of the model.
