  We recall some well and some less known results about the Kodama state and
the related $\theta$ ambiguity in defining canonical variables. Based on them,
we make some comments highlighting that the Kodama state for real connection
variables can be given a precise meaning and that it implements a vacuum peaked
on a (in a suitable sense) maximally symmetric geometry. We also highlight the
similarity of this construction with the isolated horizon boundary condition $F
\propto \Sigma$ and stress that it is, in agreement with earlier work,
inadequate to define the notion of a quantum horizon.
