# Is every coNP-complete language P-isomorphic to an P-immune coNP-complete language? OR Is there a P-immune coNP-complete language?

A set is $\mathsf{P}$-immune iff it has no non-trivial $\mathsf{P}$ subset.

Is every $\mathsf{coNP}$-complete language $\mathsf{P}$-isomorphic to an $\mathsf{P}$-immune $\mathsf{coNP}$-complete language?

Joshua Grochow's answer to my previous questions shows the answer is negative assuming cryptographic conjectures. Is it possible to show the answer is negative only assuming $\mathsf{P}\neq\mathsf{NP}$?