Conjecture on the complexity of the k-general d-position problem

The $k$-general $d$-position problem takes as input a graph $G$, integers $k\geq 2$ and $d\geq 1$, and a positive integer $r$, and asks whether $\mathrm{gp}^k_d(G)$ is greater than $r$. Complexity conjecture. The $k$-general $d$-position problem is $\operatorname{NP}$-complete. This conjecture is motivated by the known NP-completeness of the general $d$-position problem. The source does not give a proof or indicate that the conjecture has been resolved.