The conjecture on the number of 5-cycles in integer distance graphs

Let $T$ be the set of positive integers under consideration in the paper, let $T_1=\{22,58,70,82,142,190,298,330,358,382,478,658,742,862,1222,1978\}$, and let $C_3(t)$ denote the number of 5-cycles in the relevant graph associated with $t$. The conjecture on 5-cycles. For all $t\in T\setminus T_1$, $C_3(t)=5$. This conjecture asserts that the exhaustive computation identifying the exceptional values $T_1$ captures every case in which the number of 5-cycles exceeds five; its validity beyond the computational range remains open.