Maximal cyclic edge-connectivity of cages

Prove that every $(k,g)$-cage is cyclically $(k-2)g$-edge-connected.

Background

For any $(k,g)$-cage with $k\ge 3$ and $g\ge 5$, removing the edges incident with a fixed $g$-cycle but not belonging to that cycle produces a cycle-separating cut of size $(k-2)g$. Thus this quantity is an upper bound on cyclic edge-connectivity. The paper proposes that every cage achieves this maximum and proves the conjecture only for cages whose order is at most $2M(k,g)-g^2$.