How is the NP verifier polynomial?
You run your NTM, and at any point where it could decide between n &gt; 1 actions, it picks an action k and writes k to a tape.
Now you build a TM. It’s identical to the NTM, except at every point where the NTM made a decision, your TM reads a number k from the NTMs successful run, and takes action #k. That’s it.