Box-dimension equality conjecture for leaves near resonant complex saddles

Let $X$ be a resonant complex saddle and let $L_a$ be any leaf of a foliation passing through $a\in\mathbb{C}^2$ close to the saddle. The preceding estimate gives a lower bound for $\dim_B(L_a)$ according to the formal type of the saddle.

Box-dimension equality conjecture. The equality holds in the displayed lower-bound formula: $\dim_B(L_a)$ equals the corresponding value in the cases listed there.

The conjecture concerns the missing upper bound for the box dimension of a leaf near a resonant complex saddle. The source explicitly leaves this upper-bound computation for future research and notes that connectedness of the leaves prevents a direct application of the planar saddle results.