  We analyze the four-point function of stress-tensor multiplets for the 6d
quantum field theory with $OSp(8^*|4)$ symmetry which is conjectured to be dual
to M-theory on $AdS_7 \times S^4$, and deduce the leading correction to the
tree-level supergravity prediction by obtaining a solution of the crossing
equations in the large-$N$ limit with the superconformal partial wave expansion
truncated to operators with zero spin. This correction corresponds to the
M-theoretic analogue of $\mathcal{R}^4$ corrections in string theory. We also
find solutions corresponding to higher-spin truncations, but they are
subleading compared to the 1-loop supergravity prediction, which has yet to be
calculated.
