The BLZ-oper no-monodromy correspondence conjecture

Let $L_0$ be the displayed BLZ-type oper, with distinct points $t_j\notin\{0,1\}$, satisfying the condition $b_0+b_1+\sum_iq_i=0$ and having monodromy-free singularities at $x=1$ and at every $x=t_j$. BLZ no-monodromy conjecture. For generic $m,k$, every such operator corresponds to an isolated solution of the Gaudin Bethe Ansatz equations. The conjecture extends the analogous Gaudin correspondence to this BLZ-type family; it is not resolved in the supplied text.