Unbounded handle complexity conjecture for connected sums of the Poincaré sphere

Let $Y_n=\#_n\Sigma(2,3,5)$, where $\Sigma(2,3,5)$ is the Poincaré homology sphere. A bounding four-manifold for $Y_n\#-Y_n$ is a four-manifold whose boundary is $Y_n\#-Y_n$. Unbounded handle complexity conjecture. The minimum number of handles in any bounding four-manifold for $Y_n\#-Y_n$ goes to infinity as $n$ goes to infinity. This would generalize the paper's lower bounds for the numbers of $1$-, $2$-, and $3$-handles, and concerns the complexity of bounding four-manifolds even though $Y_n\#-Y_n$ bounds an integer homology ball.