GRR density conjecture for fixed-valency Cayley graphs

For fixed $d\geq 3$, let $CAY_d(n)$ be the number of isomorphism classes of $d$-valent Cayley graphs of order at most $n$, and let $GRR_d(n)$ count those that are graphical regular representations. GRR density conjecture. For every $d\geq 3$,

$$\frac{GRR_d(n)}{CAY_d(n)}\to 1 \qquad (n\to\infty).$$

This asserts that almost all fixed-valency Cayley graphs are GRRs under the paper's enumeration convention. The source contrasts this with a generating-set proportion formulation and leaves the graph-counting version open.