Smale's sixth problem for generic masses

Let $n$ bodies have masses $m_1,\dots,m_n$ and pairwise distances $r_{ij}$ satisfying the Albouy–Chenciner equations and the Cayley–Menger equations for planar configurations. A normalization removes the scaling freedom, and a normalized central configuration is a central configuration represented by one such normalized distance vector. Smale's sixth-problem conjecture for generic masses. For generic values of the masses, the number of normalized central configurations in the $n$-body problem over any field of characteristic $0$ is finite. The conjecture extends Smale's question from positive real masses and real configurations to generic masses and configurations over arbitrary characteristic-zero fields; the supplied text does not state whether it has been resolved.