$\mathsf{UP} \neq \mathsf{EXP}$ is open. A UP-generic oracle should make $\mathsf{P} \neq \mathsf{UP} = \mathsf{EXP}$, and since $\mathsf{UP} \subseteq \mathsf{\oplus P}$ relative to any oracle, this should resolve 1.
Joshua Grochow
- 38.5k
- 4
- 134
- 233