The interval conjecture for general position spectra

Let $G$ be a graph, and let

$$S_{{\rm gp}}(G)=\{\,{\rm gp}(D):D\text{ is an orientation of }G\,\}$$

be its general position spectrum. The interval-spectrum conjecture. The set $S_{{\rm gp}}(G)$ is an interval of integers. The spectrum is an interval for all graphs computed in the paper, but the general assertion remains open.