Yes, that&#x27;s right.<p>The paper doesn&#x27;t explain in detail how the gadgets are assembled. But presumably the track is arranged so that from the starting point the car must enter the variable gadget for X1. The &quot;true&quot; branch for X1 then visits each clause gadget containing X1, and the false branch visits each clause gadget containing ¬X1. These two branches must then come together somehow (no gadget is given, but it&#x27;s easy to see how to make one), and then enter the variable gadget for X2, and so on.<p>So if the car could steer in mid-air, then it would be able to jump from ¬X3 (say) back to X1, and this would allow it to repeat the track for the X2 and X3 variables, and it could make a different choice on the second run through, thus making its path no longer correspond to a 3SAT solution.