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We establish the Hatsugai-Kohmoto model as a stable quartic fixed point(distinct from Wilson-Fisher) by computing the $\beta-$function in the presenceof perturbing local interactions. In vicinity of the half-filled doped Mottstate, the $\beta-$function vanishes for all local interactions regardless oftheir sign. The only flow away from the HK model is through the superconductingchannel which lifts the spin degeneracy as does any ordering tendency. Thesuperconducting instability is identical to that establishedpreviously\cite{nat1}. A corollary of this work is that Hubbard repulsiveinteractions flow into the HK stable fixed point in the vicinity ofhalf-filling. Consequently, although the HK model has all-to-all interactions,nothing local destroys it. The consilience with Hubbard arises because bothmodels break the $Z_2$ symmetry on a Fermi surface, the HK model being thesimplest to do so. Indeed, the simplicity of the HK model belies its robustnessand generality.

Proof of a Stable Fixed Point for Strongly Correlated Electron Matter