  We establish the Hatsugai-Kohmoto model as a stable quartic fixed point
(distinct from Wilson-Fisher) by computing the $\beta-$function in the presence
of perturbing local interactions. In vicinity of the half-filled doped Mott
state, the $\beta-$function vanishes for all local interactions regardless of
their sign. The only flow away from the HK model is through the superconducting
channel which lifts the spin degeneracy as does any ordering tendency. The
superconducting instability is identical to that established
previously\cite{nat1}. A corollary of this work is that Hubbard repulsive
interactions flow into the HK stable fixed point in the vicinity of
half-filling. Consequently, although the HK model has all-to-all interactions,
nothing local destroys it. The consilience with Hubbard arises because both
models break the $Z_2$ symmetry on a Fermi surface, the HK model being the
simplest to do so. Indeed, the simplicity of the HK model belies its robustness
and generality.
