The exact L(3,2,1)-labeling number of odd 4-valent circulants with steps 1 and 5

Let $n\in\mathbb{N}$ be odd with $n\geq105$, and let $G=C_n(\\{1,5,n-5,n-1\\})$. The invariant $\lambda_{(3,2,1)}(G)$ is the minimum span of an $L(3,2,1)$-labeling of $G$, meaning a labeling of the vertices by nonnegative integers such that labels of vertices at distances $1$, $2$, and $3$ differ by at least $3$, $2$, and $1$, respectively.

Exact labeling-number conjecture.

$$\lambda_{(3,2,1)}(G)=14.$$

The source constructs an $L(3,2,1)$-labeling with span $14$ for the stated range, while computer tests found no labeling with labels $0,1,\ldots,13$ for odd $n\leq101$. Thus the conjecture combines the construction with the expected lower bound for all odd $n\geq105$.