Cyclic 5-connectivity conjecture for the T families

Let $T^1_\alpha(m;a,a,c)$, $T^1_\beta(m;a,a,c)$, and $T^2_\alpha(m;a,a,c)$ be the snark families defined from the two triangle-destroying deletions of the Petersen-derived 5-pole. Cyclic 5-connectivity conjecture. If $m/\gcd(m,c)>4$, then the infinite families of snarks $T^1_\alpha(m;a,a,c)$ and $T^1_\beta(m;a,a,c)$ are cyclically 5-connected. The text reports computational checks for several small cases, but no general proof is given.