Summary: Conclusive mathematical arguments are presented supporting the ratchet conjecture [R. Chacón, J. Phys. A, Math. Theor. 40, No. 22, F413–F419 (2007; Zbl 1114.81050)], i.e. the existence of a universal force waveform which optimally enhances directed transport by symmetry breaking. Specifically, such a particular waveform is shown to be unique for both temporal and spatial biharmonic forces, and general (non-perturbative) laws providing the dependence of the strength of directed transport on the force parameters are deduced for these forces. The theory explains previous results for a great diversity of systems subjected to such biharmonic forces and provides a universal quantitative criterion to optimize any application of the ratchet effect induced by symmetry breaking of temporal and spatial biharmonic forces.