Derrida's conjecture for the critical resistance scaling constant

Let $R_n$ be the resistance in the critical resistance model, let $p_c=\frac12$, and let $c_{\mathrm{eff}}$ be the constant in the critical scaling conjecture for $\log R_n$. Derrida's conjecture. The preceding conjecture should hold with

$$c_{\mathrm{eff}}=9\zeta(3),\qquad \zeta(3)=\sum_{n=1}^{\infty}\frac1{n^3}.$$

This is a refinement of the Addario-Berry et al. prediction, specifying its otherwise undetermined scaling constant; the source gives no resolution.