The susceptibility upper-bound conjecture for anisotropic percolation

Consider a bond percolation model on $\mathbb{Z}^d\times\mathbb{Z}^{s}$ with parameters $(p,q)$, where $p<p_c(d)$. Let $q_c(p)$ be the critical value of $q$, and let $\chi_d(p)$ denote the susceptibility for bond percolation on $\mathbb{Z}^d$. Susceptibility upper-bound conjecture. There exists a constant $\beta>0$ such that

$$q_c(p)\leq\frac{\beta}{\chi_d(p)}.$$

The conjecture is presented as a sufficient upper bound that, together with an earlier theorem and the stated validity of another equation, would imply equality of the critical exponents $\psi(d)$ and $\gamma(d)$. The supplied text gives no resolution status.