2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225354In the present paper we refute the criticism advanced in a recent preprint by Figueiredo et al [1] about the possible application of the $q$-generalized Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model. We exhibit that, contrary to what is claimed by these authors and in accordance with our previous results, $q$-Gaussian-like curves are possible and real attractors for a certain class of initial conditions, namely the one which produces nontrivial longstanding quasi-stationary states before the arrival, only for finite size, to the thermal equilibrium.2 pages, 2 figures. Short version of the paper, accepted for publication in Europhysics Letters, (2009) in pressStatistical Mechanicstext