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In this paper, we take a closer look at Czerwinski's "${\rm P}\neq{\rm NP}$relative to a ${\rm P}$-complete oracle" [Cze23]. There are (uncountably)infinitely-many relativized worlds where ${\rm P}$ and ${\rm NP}$ differ, andit is well-known that for any ${\rm P}$-complete problem $A$, ${\rm P}^A \neq{\rm NP}^A \iff {\rm P}\neq {\rm NP}$. The paper defines two sets ${\rm D}_{\rmP}$ and ${\rm D}_{\rm NP}$ and builds the purported proof of their main theoremon the claim that an oracle Turing machine with ${\rm D}_{\rm NP}$ as itsoracle and that accepts ${\rm D}_{\rm P}$ must make $\Theta(2^n)$ queries tothe oracle. We invalidate the latter by proving that there is an oracle Turingmachine with ${\rm D}_{\rm NP}$ as its oracle that accepts ${\rm D}_{\rm P}$and yet only makes one query to the oracle. We thus conclude that Czerwinski'spaper [Cze23] fails to establish that ${\rm P} \neq {\rm NP}$.

On Czerwinski's "${\rm P} \neq {\rm NP}$ relative to a ${\rm P}$-complete oracle"