The local product structure conjecture for the core of a quasi-solenoidal component

Let $\Lambda$ be a quasi-solenoidal component of the Julia set, and define its core by

$$\operatorname{Core}(\Lambda)=\left\{x\in\Lambda,\ N^u(x)\geq 2\right\}.$$

A point $x\in\operatorname{Core}(\Lambda)$ is regular if $N^u(x)=2$.

Core local product structure conjecture. The set $\operatorname{Core}(\Lambda)$ has local product structure near any regular point, and is locally the product of a Jordan arc by a totally disconnected set.

The core is introduced as a closed hyperbolic invariant set, and the stated local product description is a natural refinement of its structure near regular points. The supplied source does not provide a resolution of this conjecture.