  We postulate an exact permutation symmetry acting on 10^32 Standard Model
copies as the largest possible symmetry extension of the Standard Model. This
setup automatically lowers the fundamental gravity cutoff down to TeV, and
thus, accounts for the quantum stability of the weak scale. We study the
phenomenology of this framework and show that below TeV energies the copies are
well hidden, obeying all the existing observational bounds. Nevertheless, we
identify a potential low energy window into the hidden world, the oscillation
of the neutron into its dark copies. At the same time, proton decay can be
suppressed by gauging the diagonal baryon number of the different copies. This
framework offers an alternative approach to several particle physics questions.
For example, we suggest a novel mechanism for generating naturally small
neutrino masses that are suppressed by the number of neutrino species. The
mirror copies of the Standard Model naturally house dark matter candidates. The
general experimentally observable prediction of this scenario is an emergence
of strong gravitational effects at the LHC. The low energy permutation symmetry
powerfully constrains the form of this new gravitational physics and allows to
make observational predictions, such as, production of micro black-holes with
very peculiar properties.
