The Gaudin no-monodromy correspondence conjecture

Let $L_1$ be the displayed scalar oper with distinct nonzero points $s_i$, integer $r$, and parameters $k,l,n_1$ as in the source. Gaudin no-monodromy conjecture. For generic $k,l$, every such operator having trivial monodromy around each $x=s_i$ for all $i$ is obtained from a solution of the exponential Gaudin Bethe Ansatz equations with $d_0-d_1=r$. This conjecture asserts the converse to the proved implication from the Bethe Ansatz equations to the trivial-monodromy equations; no resolution is given in the supplied text.