The closedness and value conjecture for the degree-three density constant

Let $d$ denote the degree of a Cayley digraph, and let $\Delta_3$ and $\Delta_3'$ be the associated density constants introduced in the paper. Degree-three density conjecture. The degree $d=3$ is closed and

$$\Delta_3=\Delta_3'=\frac{21}{250}.$$

The conjecture is motivated by numerical evidence comparing the extremal function $\kappa(3,n)$ with the lower bound $\ell'(3,n)$, including computed examples of dilated Cayley digraphs. The supplied text does not indicate whether the conjecture has been resolved.