Component-count conjecture for $J_{10}^1$ singularities

Let $f_0$ be a real function singularity of type $J_{10}^1$. Consider the discriminant variety in the parameter space of any versal deformation of $f_0$. Six representative topological types are shown in Fig. J101; five further types are obtained from the non-leftmost five by reflection in a horizontal mirror and simultaneous change of all signs.

$J_{10}^1$ component conjecture. The complement of the discriminant variety has exactly 11 components, represented by these six original and five transformed topological types.

The preceding proposition describes ten virtual components and the involution relating them. The assertion is the corresponding completeness and distinctness claim for actual components of the discriminant complement.