Global resilience conjecture for odd cycles in pseudorandom graphs

Let $k\geq 5$ be an odd integer and let $G$ be an $(n,d,\lambda)$-graph satisfying

$$d^{k-1}/n\gg \lambda^{k-2}.$$

Global resilience conjecture. Then $G$ has global resilience $(1/4+o(1))nd$ with respect to being $C_k$-free.

This conjecture is presented as a natural generalization of the global resilience form of an earlier theorem. Its validity would extend the paper's resilience results from the established cases to all odd cycle lengths $k\geq 5$.