Voronoi decomposition conjecture for tropical Prym second moments

Let $R_{\widetilde{G}/G}$ be the cone associated with a double cover $\widetilde{G}\to G$. As a double cover of tropical curves $\widetilde{\Gamma}\to\Gamma$ varies over $R_{\widetilde{G}/G}$, consider the second moment $I_2(\operatorname{Prym}(\widetilde{\Gamma}/\Gamma))$ of its tropical Prym variety. Voronoi decomposition conjecture. The Voronoi decomposition of the cone $R_{\widetilde{G}/G}$ is given by the domains of polynomiality of

$$I_2(\operatorname{Prym}(\widetilde{\Gamma}/\Gamma)).$$

The conjecture aims to identify the minimal toric decomposition relevant to resolving the Prym--Torelli map. The source explains that the previously constructed decomposition can be strictly finer than the Voronoi decomposition, while the proposed characterization remains unresolved.