The conjecture on odd girth of rational three-dimensional distance graphs

Let $T$ be the set of positive integers under consideration, and let $G(\mathbb{Q}^3,\sqrt{t})$ denote the graph whose vertices are points of $\mathbb{Q}^3$ with adjacency determined by Euclidean distance $\sqrt{t}$. The odd girth of a graph is the length of its shortest odd cycle. The rational-space odd-girth conjecture. For all $t\in T$, the graph $G(\mathbb{Q}^3,\sqrt{t})$ has odd girth $5$. This is proposed as an analogue in rational three-dimensional space of the paper's earlier conjecture for the corresponding integer setting; the supplied text gives no resolution, so the claim remains open.