  We construct an infinite commutative lattice of groups whose dual spaces give
Kauffman finite-type invariants of long virtual knots. The lattice is based
"horizontally" upon the Polyak algebra and extended "vertically" using
Manturov's functorial map $f$. For each $n$, the $n$-th vertical line in the
lattice contains an infinite dimensional subspace of Kauffman finite-type
invariants of degree $n$. Moreover, the lattice contains infinitely many
inequivalent extensions of the Conway polynomial to long virtual knots, all of
which satisfy the same skein relation. Bounds for the rank of each group in the
lattice are obtained.
