The Cohen–Lenstra rationality conjecture for motivic curve zeta series

Let $X$ be a reduced curve over $\mathbb{F}_q$, and let $\widetilde X$ be its normalization. Let $\#_q$ denote the point-count homomorphism from the completed Grothendieck ring to $\mathbb{Q}$. The Cohen–Lenstra rationality conjecture.

$$\#_q\left(\frac{\widehat{Z}^\mathrm{mot}_X(t)}{\widehat{Z}^\mathrm{mot}_{\widetilde X}(t)}\right)\in\mathbb{Q}[[t]]$$

is a power series in $t$ with infinite radius of convergence.

The conjecture generalizes the proved nodal case and predicts an entire point-count numerator for every reduced curve. Its cusp case is discussed as a consequence of the later cusp conjectures.