Deformation invariance of solitary points on maximally inflected plane quintics

A maximally inflected plane quintic is a real rational curve of degree $5$ in $\mathbb{P}^2$ whose ramification occurs only at real points; a solitary point is an isolated real node with conjugate tangent directions. Deformation-invariance conjecture. The number of solitary points in a maximally inflected plane quintic is invariant under deformation. The claim is motivated by computations suggesting that this number depends only on the necklace, rather than on the placement of the ramification points; it remains a conjecture in the source.