Full elasticity conjecture for cyclic rational semirings

Let $r\in\mathbb{Q}_{>1}\setminus\mathbb{N}$, and write $r=\mathsf{n}(r)/\mathsf{d}(r)$ in lowest terms. Let $S_r$ be the cyclic rational semiring generated by the geometric sequence determined by $r$. A monoid is fully elastic if its set of elasticities is all of $\mathbb{Q}_{\geq 1}\cup\{\infty\}$. Full elasticity conjecture. If

$$\mathsf{n}(r)>\mathsf{d}(r)+1,$$

then $S_r$ is fully elastic. The preceding result establishes density of the set of elasticities under the same condition on $r$, but full elasticity requires realizing every permitted elasticity and remains open.