  The ultraviolet divergences of amplitude diagrams in maximal supergravity are
characterised by a first possible divergence at seven loops for the 4-point
amplitude (logarithmic) and, in its absence, at eight loops. We revisit the
pure spinor superfield theory results of [arXiv:1412.5983], stating the absence
of the divergence originating in the 4-point 7-loop amplitude as well as those
of more than seven loops. The analysis, performed in terms of the one-particle
irreducible loop structures giving rise to the divergences, is extended,
especially with respect to the limits on the dimension for finiteness. The
results correspond to those mentioned, known from other approaches, indicating
an ultraviolet finiteness of maximal supergravity in D=4.
