Topological graded ideal zeta function at infinity conjecture

Assume the uniformity conjecture, so that the reduced graded ideal zeta function $\zeta_{\mathfrak{f}_{c,d},\operatorname{red}}^{\triangleleft_{\operatorname{gr}}}(Y)$ is defined. Let $r=\operatorname{rk}_{\mathbb{Z}}(\mathfrak{f}_{c,d})$. Topological-at-infinity conjecture.

$$\left.s^{-r}\zeta_{\mathfrak{f}_{c,d},\operatorname{top}}^{\triangleleft_{\operatorname{gr}}}(s^{-1})\right|_{s=0}=\left.(1-Y)^r\zeta_{\mathfrak{f}_{c,d},\operatorname{red}}^{\triangleleft_{\operatorname{gr}}}(Y)\right|_{Y=1}\in\mathbb{Q}_{>0}.$$

The source explicitly singles out this conjecture as unresolved for $c=2$ and $d\geq5$; it has relevant special-case confirmations.