Simplicity conjecture for generalized Laguerre polynomial zeros

Let $b1>-1$, let $bb$ be an even partition, and let $bc$ be the partition parameter occurring in the generalized Laguerre polynomial $a9_{bb,bc}^{(b1)}$. The zeros of $a9_{bb,bc}^{(b1)}$ are the zeros under consideration. Simplicity conjecture. All these zeros are simple. The conjecture is offered on the basis of numerical evidence and is needed in the paper's asymptotic result describing how zeros of the generalized Laguerre polynomial attract exceptional zeros. Its resolution is not given in the source.