Dimensional crossover critical exponent conjecture for anisotropic bond percolation

Let $q_c:[0,1]\to[0,1]$ be the critical function for anisotropic bond percolation, and let $p_c(d)$ denote the critical parameter for $d$-dimensional percolation. Write $a(p)\approx b(p)$ when $\log a(p)/\log b(p)\to1$ as $p\uparrow p_c(d)$. A critical exponent $\gamma(d)>0$, when it exists, is defined by the susceptibility asymptotic $\chi_p(d)\approx|p-p_c(d)|^{-\gamma(d)}$. Dimensional crossover critical exponent conjecture. There exists a critical exponent $\psi=\psi(d)>0$, depending only on $d$, such that

$$q_c(p)\approx|p-p_c(d)|^{\psi}.$$

Moreover, if $\gamma(d)$ exists, then $\psi(d)=\gamma(d)$. This conjecture predicts the relationship between the critical curve and susceptibility near the lower-dimensional critical point, and concerns the dimensional crossover from $d$ to $d+s$ dimensions.