Polynomial bound conjecture for the Schrijver number of the square of the Kneser graph

Let $G_n$ be the Schrijver graph, and let $G_n^{\boxtimes 2}$ denote its strong square. The Schrijver number of a graph $G$, denoted by $\vartheta'(G)$, is the corresponding strengthened Lovász theta number. Polynomial Schrijver-number conjecture. There exists an absolute constant $C>0$ such that

$$\vartheta'(G_n^{\boxtimes 2})\le n^C.$$

This conjecture asks for a substantially tighter bound on the Schrijver number of the strong square of the Schrijver graph, beyond the bounds obtained from multiplicative Lovász theta-number methods. Its status is not resolved in the supplied text.