The Galois-conjugate description of the principal-vein Master Teapot

For coprime integers $(p,q)$, let $\Theta^{per}_{p/q}$ denote the set of angles associated to critically periodic parameters in the principal $p/q$-vein, let $h(\theta)$ be the core entropy, and let $z$ be a Galois conjugate of a real number $\lambda$. Define

$$\Upsilon_{p/q} = \overline{\\{ (z, \lambda) \in \mathbb{C} \times \mathbb{R} \mid \lambda = e^{h(\theta)} \textrm{ for some } \theta \in \Theta^{per}_{p/q}, z \textrm{ is a Galois conjugate of }\lambda \\}}.$$

The principal-vein Master Teapot conjecture. The set $\Upsilon_{p/q}$ is given by the closure of the pairs consisting of $e^{h(\theta)}$ and its Galois conjugates, as displayed above. This conjecture proposes that the Galois-conjugate version of the Master Teapot is captured by the entropy data of critically periodic angles in each principal vein. The supplied text does not state evidence of resolution.