Zhang's unified conjecture for polarized metrized graphs

Let $\Gamma$ be an irreducible polarized metrized graph of genus $\bar{g}\geq2$, with total length $\ell(\Gamma)$, invariants $a(\Gamma)$ and $\epsilon(\Gamma)$, and let $c(\bar{g})$ be a positive number for each $\bar{g}\geq2$. Zhang's unified conjecture. The following two inequalities hold:

$$\frac{\bar{g}-1}{\bar{g}+1}\bigl(\ell(\Gamma)-4\bar{g}\,a(\Gamma)\bigr)\leq\epsilon(\Gamma)\leq12\bar{g}\,a(\Gamma)-(1+c(\bar{g}))\ell(\Gamma).$$

Zhang introduced this formulation to reduce and unify his first and second conjectures; the source gives no resolution status.