Jain's connectivity and diameter conjecture for unit graphs over $\mathbb{Z}_n$

Let $n$ be a natural number, and let $G(\mathbb{Z}_n)$ be the unit graph. Write $U(\mathbb{Z}_n)$ for its set of units, $N_U(\mathbb{Z}_n)$ for its set of non-units, and $\operatorname{diam}(G(\mathbb{Z}_n))$ for the graph diameter. Jain's conjecture. The graph $G(\mathbb{Z}_n)$ is connected, and

$$2\in U(\mathbb{Z}_n)\quad\Longrightarrow\quad \operatorname{diam}(G(\mathbb{Z}_n))\leq 2,$$

while

$$2\in N_U(\mathbb{Z}_n)\quad\Longrightarrow\quad \operatorname{diam}(G(\mathbb{Z}_n))\leq 3.$$

The conjecture concerns the connectivity and metric structure of unit graphs for arbitrary natural $n$. The surrounding paper states that these assertions are resolved there, so this candidate is treated as solved.