Is a quadratic nondeterminism speed-up of deterministic computation plausible?
Note that even a result along the lines of $\mathsf{DTime}(\tilde{O}(n^2)) \subseteq \mathsf{NTime}(n^{2-\epsilon})$ would violate NSETH as univariate polynomial identity testing (as defined in section 3.2) can be solved in $\tilde{O}(n^2)$ time deterministically, but there doesn't seem to be an obvious way to use nondeterminism to help prove identity.