The stronger minimum pseudocodeword weight bound for expander codes

Let $G$ be a $(c,d,m,n,\mu)$ expander graph, and let $N$ denote the block length of the LDPC code obtained from $G$. Let $w^{BSC}_{\min}$ denote its minimum pseudocodeword weight. Assume that

$$\epsilon_2d\geq \epsilon_1c>2\mu.$$

Stronger pseudocodeword weight conjecture. The resulting LDPC code has

$$w^{BSC}_{\min}\geq N\left(\frac{\epsilon_1\epsilon_2}{2}-\frac{\mu}{2\sqrt{cd}}\left(\epsilon_1\sqrt{\frac{c}{d}}+\epsilon_2\sqrt{\frac{d}{c}}\right)\right).$$

The authors present this as a strengthening of the preceding lower bound for the minimum pseudocodeword weight; the supplied text gives no evidence that it has been proved or disproved.