I am a Ph.D. student studying CS theory, I made this account for this question.
Recently, I seem to have obtained a proof of existence of a PRP (which is unconditional in the sense that it does not rely on unproven assumptions), but in order for it to work it does require a limitation of the running time of the adversary. That is, in a usual setting, for security parameter $n$, the assumption normally goes that the adversary can run in time $an^c$ for arbitrary (positive) constants $a, c$. So in the case of distinguishing a PRP from a random permutation, they can make $an^c$ queries to the oracle.
I have constructed a PRP which I can show no adversary can distinguish from a random permutation, so long as $c<1$. That is, if the adversary does not run more than $an^c$ oracle queries, where $a$ is arbitrary and $c$ is less than 1, then I can prove the adversary cannot distinguish the PRP from a random permutation. But as soon as $c\geq 1$ all bets are off and the proof does not work.
I realize that this result is quite weak, so I wanted to ask here if this would be worth sharing with my advisor. I do not want to embarress myself by sharing a result like this with my advisor, when it is probably useless and not interesting. But just in case the (theoretical) community would find it interesting, I wanted to check here.