The generic-rank conjecture for bipartite circulant graphs

Let $G(n,l)$ be a bipartite circulant graph of the form considered in the paper, and let the generic completion rank be the rank attained by a generic matrix completion. The dimension-count prediction is

$$n- \left\lfloor\sqrt{n^2-nl}\right\rfloor.$$

Bipartite circulant generic-rank conjecture. Every graph $G(n,l)$ has generic completion rank predicted by the dimension count; equivalently,

$$\operatorname{gcr}(G(n,l))=n-\left\lfloor\sqrt{n^2-nl}\right\rfloor.$$

The paper proves the dimension-count prediction for a subset of these graphs and conjectures it for all bipartite circulant graphs of this form. The claim is presented as unresolved.