The presence of floating-point roundoff errors compromises the results of virtually all fast mixed-integer programming solvers available today. In this talk we present recent advances in our endeavour to craft a performant mixed-integer optimizer that is not only free from roundoff errors, but also produces certificates of optimality that can be verified independently of the solving process. We provide an overview of the entire framework, which is an extension of the open solver SCIP. We focus in particular on the safe generation and verification of Gomory mixed-integer cuts via mixed-integer rounding. This is joint work with Sander Borst, Leon Eifler, Fabian Frickenstein, and Jules Nicolas-Thouvenin.