Farber–Oprea rationality conjecture for the TC-generating function

Let $X$ be a finite CW complex, and define its $4\operatorname{\mathsf{TC}}4$-generating function by

$$f_X(t)=\sum_{m=1}^{\infty} \operatorname{\mathsf{TC}}_{m+1}(X)\hspace{1mm}t^m.$$

Farber–Oprea conjecture. The formal power series $f_X(t)$ represents a rational function of the form

$$\frac{P_X(t)}{(1-t)^2},$$

where $P_X(t)$ is an integral polynomial satisfying $P_X(1)=\operatorname{cat}(X)$. This conjecture is verified in the paper for symmetric products of closed orientable surfaces, but remains open for finite CW complexes in general.