Furstenberg dimension conjecture for sine wave and circular sets

Let $0<u\leq1$ and $0\leq v\leq3$. A sine wave $(u,v)$-Furstenberg set or circular $(u,v)$-Furstenberg set is a set $F\subseteq\mathbb{R}^2$ of the type specified in the paper, with parameters $u$ and $v$. Furstenberg dimension conjecture. Such a set should satisfy

$$\dim F\geq \begin{cases} u+v & 0\leq v\leq u,\\ \frac{5u+v}{3} & 0\leq u<v\text{ and }2u+v\leq3,\\ u+1 & 2u+v>3, \end{cases}$$

or equivalently

$$\dim F\geq\min\left\{u+v,\frac{5u+v}{3},u+1\right\}.$$

This is proposed as a Furstenberg analogue of the restricted projection conjecture. The first case is known, and product-set examples support the $u+1$ term when $2u+v>3$; the remaining asserted bounds are not established in the source.