The bounded realization problem is a2^P-complete

The bounded realization problem asks whether a valid realization exists subject to the specified bounds on the weights of the cycles. Bounded realization conjecture. The bounded realization problem is $\Sigma_2^{P}$-complete. This is motivated by the fact that the problem lies in $\Sigma_2^{P}$ while checking validity of a proposed answer is already $coNP$-complete; its $\Sigma_2^{P}$-hardness remains open.