  Because Fermi liquids are inherently non-interacting states of matter, all
electronic levels below the chemical potential are doubly occupied.
Consequently, the simplest way of breaking Fermi liquid theory is to engineer a
model in which some of those states are singly occupied keeping time-reversal
invariance intact. We show that breaking an overlooked local-in-momentum space
$\mathbb Z_2$ symmetry of a Fermi liquid does precisely this. As a result,
while the Mott transition from a Fermi liquid is correctly believed to obtain
without the breaking of any continuous symmetry, a discrete symmetry is broken.
This symmetry breaking serves as an organizing principle for Mott physics
whether it arises from the tractable Hatsugai-Kohmoto (HK) model or the
intractable Hubbard model. That both are controlled by the same fixed point we
establish through a renormalization group analysis. An experimental
manifestation of this fixed point is the onset of particle-hole asymmetry, a
widely observed phenomenon in strongly correlated systems. Theoretically, the
singly-occupied region of the spectrum gives rise to a surface of zeros of the
single-particle Green function, denoted as the Luttinger surface. Using
K-homology, we show that the Bott topological invariant guarantees the
stability of this surface to local perturbations. Our proof demonstrates that
the strongly coupled fixed point only corresponds to those Luttinger surfaces
with co-dimension $p+1$ with $p$ odd. We conclude that the Hubbard and HK
models both lie in the same high temperature universality class and are
controlled by the broken $\mathbb Z_2$ symmetry quartic fixed point.
