Conjecture on the real rank boundary of ternary quartics

Let $f$ be a ternary quartic, let $C(f)$ be its middle catalecticant, and let $\operatorname{disc}(f)$ and $\operatorname{Bdisc}(f)$ denote respectively the discriminant and the Blekherman discriminant. Let $\partial_{\rm alg}(\mathcal{R}_4)$ be the algebraic real rank boundary in $\mathbb{P}^{14}$. Quartic real rank boundary conjecture. The boundary is a reducible hypersurface of degree

$$84=6+27+51,$$

with three irreducible components, and algebraically

$$\partial_{\rm alg}(\mathcal{R}_4)=\operatorname{det}(C(f))\cdot\operatorname{disc}(f)\cdot\operatorname{Bdisc}(f).$$

This conjecture identifies the three expected boundary components: the catalecticant determinant, the discriminant, and the Blekherman discriminant. The source gives no resolution status.