  We present a procedure for the determination of the mass of the top quark at
the LHC based on leptonic observables in dilepton $t\bar{t}$ events. Our
approach utilises the shapes of kinematic distributions through their few
lowest Mellin moments; it is notable for its minimal sensitivity to the
modelling of long-distance effects, for not requiring the reconstruction of top
quarks, and for having a competitive precision, with theory errors on the
extracted top mass of the order of 0.8 GeV. A novel aspect of our work is the
study of theoretical biases that might influence in a dramatic way the
determination of the top mass, and which are potentially relevant to all
template-based methods. We propose a comprehensive strategy that helps minimise
the impact of such biases, and leads to a reliable top mass extraction at
hadron colliders.
