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The nucleus is an extraordinarily complex object where fundamental forces are at work. The solution of this many-body problem has challenged physicists for decades: several models with complementary virtues and flaws have been adopted, none of which has a universal predictive capability. Double beta decay is a second-order weak nuclear decay whose precise measurement might steer fundamental improvements in nuclear theory. Its knowledge paves the way to a much better understanding of many-body nuclear dynamics and clarifies, in particular, the role of multiparticle states. This is a useful input to a complete understanding of the dynamics of neutrino-less double beta decay, the chief physical process whose discovery may shed light to the matter-antimatter asymmetry of the universe and unveil the true nature of neutrinos. Here, we report the study of $2νββ$-decay in $^{82}$Se with the CUPID-0 detector, an array of ZnSe crystals maintained at a temperature close to 'absolute zero' in an ultralow background environment. Thanks to the unprecedented accuracy in the measurement of the two electrons spectrum, we prove that the decay is dominated by a single intermediate state. We obtain also the most precise value for the $^{82}$Se $2νββ$-decay half-life of $T^{2ν}_{1/2} = [8.6^{+0.2}_{-0.1}] \times 10^{19}$ yr.