A Problem on Time Complexity of Algorithms
For $k = \left\lceil \dfrac{r}{2} \right\rceil$, it is conjectured (and proven in some simpler models of computation by JeffE) that $r$-SUM problem has lower bounds $\Omega(n^k)$, the solution for which can be verified in $O(n)$ time.

Pick an $r$ such that $k \gt t$, implying $\omega(n^t)$ bounds.