  According to the recent pure spinor analysis of the UV divergences by
Karlsson, there are no divergent 1PI structures beyond 6 loops in D=4 N=8
supergravity. In combination with the common expectation that the UV
divergences do not appear at less than 7 loops, this may imply that the 4-point
amplitude in D=4 N=8 supergravity is all-loop finite. This differs from the
result of the previous studies of pure spinors, which suggested that there is a
UV divergence at 7 loops in D=4. Therefore an independent investigation of the
pure spinor formalism predictions is desirable, as well as continuation of
explicit loop computations. In the meantime, we revisit here our earlier
arguments on UV finiteness of N=8 supergravity based on the absence of the
off-shell light-cone superspace counterterms, as well as on the E_{7(7)}
current conservation. We believe that both arguments remain valid in view of
the developments in this area during the last few years.
