  Given a connect sum of link diagrams, there is an isomorphism which
decomposes unnormalized Khovanov chain groups for the product in terms of
normalized chain groups for the factors; this isomorphism is straightforward to
see on the level of chains. Similarly, any plumbing $x*y$ of Kauffman states
carries an isomorphism of the chain subgroups generated by the enhancements of
$x*y$, $x$, $y$:
  \[
  \mathcal{C}_R(x*y)\to
  \left(\mathcal{C}_{R,p\to1}(x)\otimes
\mathcal{C}_{R,p\to1}(y)\right)\oplus\left(\mathcal{C}_{R,p\to0}(x)\otimes
\mathcal{C}_{R,p\to0}(y)\right). \] We apply this plumbing of chains to to
prove that every homogeneously adequate state has enhancements $X^\pm$ in
distinct $j$-gradings whose $A$-traces (which we define) represent nonzero
Khovanov homology classes over $\mathbb{F}_2$, and that this is also true over
$\mathbb{Z}$ when all $A$-blocks' state surfaces are two-sided. We construct
$X^\pm$ explicitly.
