Quasi-polynomiality conjecture for cohomology of finitely generated $\mathrm{FI}_d$-modules

Let $\bk$ be an arbitrary field. Let $\FI_d$ be the category whose objects are finite sets and whose morphisms are injections with $d$-coloring of the complement: a morphism from $A$ to $B$ is a pair $(g,h)$, where $g\colon A\to B$ is an injection and $h\colon B\setminus g(A)\to [d]$ is a function. Let $V$ be a finitely generated $\FI_d$-module over $\bk$. Quasi-polynomiality conjecture. For every $t$, the function

$$n\longmapsto \dim_{\bk} H^t(\fS_n,V_n)$$

is a quasi-polynomial in $n$ of degree at most $d-1$.

This extends the expected eventual periodicity and polynomial behavior of cohomology for finitely generated FI-modules to the colored category $\FI_d$. The supplied source does not state whether the conjecture has been resolved.