Oracle comparing $EXP$ with $UP$ Heller (Theorem 6) gave an oracle relative to which $NP=EXP$, and Homer &amp; Selman gave an oracle relative to which $P=UP$ and $\Sigma_2^P=EXP$.
Beigel, Buhrman, Fortnow (freely available author's version) gave an oracle in which $P=\oplus P$ and $NP=EXP$ holds.


Is there an oracle that gives $P\neq UP=coUP=NP=coNP=\oplus P=EXP$?

Is there an oracle that gives $P=UP=coUP\neq NP=coNP=\oplus P=EXP$?



Or is it known $UP\neq EXP$ unconditionally?
$\mathsf{UP} \neq \mathsf{EXP}$ is open. A UP-generic oracle* should make $\mathsf{P} \neq \mathsf{UP} = \mathsf{EXP}$, and since $\mathsf{UP} \subseteq \mathsf{\oplus P} \subseteq \mathsf{EXP}$ relative to any oracle, this should resolve 1. (I say "should" because I haven't checked all the details...)

*UP-generic oracles are discussed, for example, by Fenner-Fortnow-Kurtz-Li (author's freely available version) and also (shameless self plug) a quick tutorial in Section 5.1 here (author's free version)