Blokh–Oversteegen–Ptacek–Timorin conjecture on the cubic main hyperbolic component

Let $\theta\in\mathbb{R}/\mathbb{Z}$. Let $\mathbf{P}^3$ be the space of conformal conjugacy classes of cubic polynomials, let $\mathbf{H}^3\subset\mathbf{P}^3$ be the hyperbolic component containing $[z^3]$, and let $\mathcal{P}^{cm}(\theta)$ be the corresponding family of cubic Siegel polynomials with rotation number $\theta$. Let $\mathcal{K}(\theta)$ be the closure of the set of non-renormalizable cubic Siegel polynomials in $\mathcal{P}^{cm}(\theta)$, and write $[\mathcal{K}(\theta)]$ for their conformal conjugacy classes. Blokh–Oversteegen–Ptacek–Timorin conjecture. For all $\theta\in\mathbb{R}/\mathbb{Z}$,

$$\overline{\mathbf{H}^3}\cap[\mathcal{P}^{cm}(\theta)]=[\mathcal{K}(\theta)].$$

This conjecture describes the intersection of the closure of the cubic main hyperbolic component with each fixed-rotation cubic Siegel family, identifying it with the corresponding central locus. The cited source attributes the conjecture to Blokh et al.; the supplied text does not state whether it has been resolved.