  The discovery of integrable $N=2$ supersymmetric Landau-Ginzburg theories
whose chiral rings are fusion rings suggests a close connection between fusion
rings, the related Landau-Ginzburg superpotentials, and $N=2$ quantum
integrability. We examine this connection by finding the natural $SO(N)_K$
analogue of the construction that produced the superpotentials with $Sp(N)_K$
and $SU(N)_K$ fusion rings as chiral rings. The chiral rings of the new
superpotentials are not directly the fusion rings of any conformal field
theory, although they are natural quotients of the tensor subring of the
$SO(N)_K$ fusion ring.
  The new superpotentials yield solvable (twisted $N=2$) topological field
theories. We obtain the integer-valued correlation functions as sums of
$SO(N)_K$ Verlinde dimensions by expressing the correlators as fusion residues.
The $SO(2n+1)_{2k+1}$ and $SO(2k+1)_{2n+1}$ related topological Landau-Ginzburg
theories are isomorphic, despite being defined via quite different
superpotentials.
