  We prove that for every $\epsilon>0$ and predicate $P:\{0,1\}^k\rightarrow
\{0,1\}$ that supports a pairwise independent distribution, there exists an
instance $\mathcal{I}$ of the $\mathsf{Max}P$ constraint satisfaction problem
on $n$ variables such that no assignment can satisfy more than a
$\tfrac{|P^{-1}(1)|}{2^k}+\epsilon$ fraction of $\mathcal{I}$'s constraints but
the degree $\Omega(n)$ Sum of Squares semidefinite programming hierarchy cannot
certify that $\mathcal{I}$ is unsatisfiable. Similar results were previously
only known for weaker hierarchies.
