Pseudocenter conjecture for entropy on Mandelbrot wakes

Let $\theta_1<\theta_2$ be external angles whose parameter rays $R_M(\theta_1)$ and $R_M(\theta_2)$ land at the same parameter on the boundary of the Mandelbrot set. Let $h(\theta)$ be the entropy of the Hubbard tree corresponding to the parameter with external angle $\theta$, and let $\theta^*$ be the pseudocenter of the interval $[\theta_1,\theta_2]$. Pseudocenter conjecture. The maximum of the entropy on this interval is attained at its pseudocenter:

$$\max_{\theta\in[\theta_1,\theta_2]}h(\theta)=h(\theta^*)$$

This conjecture connects the combinatorial entropy of Hubbard trees with the geometry of wakes in the Mandelbrot set. The supplied text gives no resolution, so the assertion remains open.