Ma, Yang, and Li's signature cycle-count conjecture

Let $G$ be a graph with signature $s(G)$, where the signature is the difference between the numbers of positive and negative eigenvalues of its adjacency matrix. Let $c_3(G)$ and $c_5(G)$ denote the numbers of cycles in $G$ whose lengths are congruent to $3$ and $1$ modulo $4$, respectively. Ma–Yang–Li conjecture.

$$-c_3(G)\leq s(G)\leq c_5(G).$$

The conjecture bounds the spectral signature using counts of cycles in two congruence classes modulo $4$. The paper attributes it to Ma, Yang, and Li and gives no resolution.