Component-count conjecture for $X_9^2$ singularities

Let $f_0$ be a real function singularity of type $X_9^2$. Consider the discriminant variety in the parameter space of an arbitrary versal deformation of $f_0$. The indicated representatives are those shown in Fig. X92, together with their negatives and their rotations through multiples of $\pi/2$.

$X_9^2$ component conjecture. These representatives exhaust the components of the complement of the discriminant variety; in total there are 52 such components.

The preceding proposition gives 18 virtual components, arranged into nine pairs, and describes the symmetry operations used to construct the proposed representatives. The conjecture asserts that these constructions account for every actual discriminant-complement component.