The large-$l$ Gaudin counting conjecture for unequal degrees

Let $r=d_0-d_1$ and use the polynomials $W_r,U_r$ and the Hermite-Wronskian polynomial $V_\mu$ defined in the source. Unequal-degree large-$l$ conjecture. For generic $l,m$, the Gaudin Bethe Ansatz system has, up to permutation of coordinates, exactly $\operatorname{Part}(d_0-r^2)$ solutions, all isolated and non-degenerate; for fixed $d_0,d_1$ there is $C\in\mathbb R$ such that $|l|,|m|>C$ implies genericity, and the solutions have the displayed partition-indexed asymptotics as $l\to\infty$. The assertion is a conjectural generalization of the equal-degree case and is not resolved in the supplied text.