Tight Low Degree Hardness for Optimizing Pure Spherical Spin Glasses

We prove constant degree polynomial algorithms cannot optimize pure spherical p-spin Hamiltonians beyond the algorithmic threshold $\operatorname{ALG} (p) = 2\sqrt {\frac{{p - 1}}{p}}$. The proof goes by transforming any hypothetical such algorithm into a Lipschitz one, for which hardness was shown previously by the author and B. Huang.