Why do reductions to NP-complete problems in NTIME(n) not break the nondeterministic time hierarchy?
The reduction takes time to perform. You know that time is polynomial but you don't know it's linear so you can't conclude that $L\in \mathrm{NTIME}(n)$. You can only conclude that $L\in\mathrm{NTIME}(n^k)$ for some&nbsp;$k$ which, of course, you already knew from the assumption that $L\in\mathrm{NTIME}(n^3)$.