  Within the histories formalism the decoherence functional is a formal tool to
investigate the emergence of classicality in isolated quantum systems, yet an
explicit evaluation of it from first principles has not been reported. We
provide such an evaluation for up to five-time histories based on exact
numerical diagonalization of the Schroedinger equation. We find a robust
emergence of decoherence for slow and coarse observables of a generic random
matrix model and extract a finite size scaling law by varying the Hilbert space
dimension over four orders of magnitude. Specifically, we conjecture and
observe an exponential suppression of coherent effects as a function of the
particle number of the system. This suggests a solution to the preferred basis
problem of the many worlds interpretation (or the set selection problem of the
histories formalism) within a minimal theoretical framework -- without relying
on environmentally induced decoherence, quantum Darwinism, Markov
approximations or ensemble averages. We further discuss the implications of our
results for the wave function of the Universe, interpretations of quantum
mechanics and the arrow(s) of time.
