  In a seminal paper, Kaminski, Kisielowski an Lewandowski for the first time
extended the definition of spin foam models to arbitrary boundary graphs. This
is a prerequisite in order to make contact to the canonical formulation of Loop
Quantum Gravity (LQG) whose Hilbert space contains all these graphs. This makes
it finally possible to investigate the question whether any of the presently
considered spin foam models yields a rigging map for any of the presently
defined Hamiltonian constraint operators.
  In the analysis of this would-be spin foam rigging map we are able to
identify an elementary spin foam transfer matrix that allows to generate any
finite foam as a finite power of the transfer matrix. However, it transpires
that the resulting object, as written, does not define a projector on the
physical Hilbert space. This statement is independent of the concrete spin foam
model and Hamiltonian constraint. Nevertehless, the transfer matrix potentially
contains the necessary ingredient in order to construct a proper rigging map in
terms of a modified transfer matrix.
