4 problems

Cut-at-vertex exterior-polynomial conjecture. For every such $\mathcal H$, $\tilde{X}_{\mathcal H}=X_{\mathcal H}$, $\tilde{X}_{\mathcal H}$ is independent of the ribbon structure,…

Exterior-polynomial analogue conjecture. Theorem-level equality and ribbon-independence asserted for the interior polynomial, as well as the cut-at-vertex conjecture for the interi…

Cut-at-vertex Bernardi conjecture. This polynomial coincides with the interior polynomial $I_{\mathcal H}$ of $\mathcal H$.

Let $(G,\rho)$ be a ribbon graph. Write $V(G)$ for its vertices, $E(G)$ for its edges, $\operatorname{Pic}^0(G)$ for its degree-zero Picard group, and $\mathcal{T}(G)\subset E(G)$…