A Critique of Sopin's "$\mathrm{P}\mathrm{H}=\mathrm{P}\mathrm{S}\mathrm{P}\mathrm{A}\mathrm{C}\mathrm{E}$"

We critique Valerii Sopin’s paper “$\mathrm{P}\mathrm{H}=\mathrm{P}\mathrm{S}\mathrm{P}\mathrm{A}\mathrm{C}\mathrm{E}$” [Sop14]. The paper claims to resolve one of the major open problems of theoretical computer science by leveraging the Skolemization of existential quantifiers of quantified boolean formulas to show that $\mathrm{Q}\mathrm{B}\mathrm{F}$ (a well-known $\mathrm{P}\mathrm{S}\mathrm{P}\mathrm{A}\mathrm{C}\mathrm{E}$-complete problem) is in ${\mathrm{\Pi }}_4^p$, and thus $\mathrm{P}\mathrm{H}=\mathrm{P}\mathrm{S}\mathrm{P}\mathrm{A}\mathrm{C}\mathrm{E}$. In this critique, we highlight problems in that paper and conclude that it fails to establish that $\mathrm{P}\mathrm{H}=\mathrm{P}\mathrm{S}\mathrm{P}\mathrm{A}\mathrm{C}\mathrm{E}$.