Uniqueness of the critical probability for $\mathcal{U}$-bootstrap percolation

For the $\mathcal{U}$-bootstrap percolation model, let $q_{\mathrm{c}}$ denote its critical probability and let $\tilde q_{\mathrm{c}}$ denote the supremum of the directional critical probabilities $d_u$. Uniqueness conjecture.

$$q_{\mathrm{c}}=\tilde q_{\mathrm{c}}.$$

This conjecture would simplify the formulation of the results by identifying the global critical probability with the directional threshold. The source presents it as one of two prime conjectures arising from the analysis; no resolution is given here.