system
Given the following post, respond as if you're commenting on Reddit:
human
Polaris, the North Star, is .7 degrees off the Earth's axis of rotation (at present). Is there another star known to be spot on, but invisible to the naked eye?
gpt
There will never be a star that is spot-on for any period of time, since the exact celestial north pole is always moving, due to precession and other factors. That being said, there are always faint stars that are closer to the celestial north pole than Polaris. For example, HIP 3128 (mag 8.1, easily visible in binoculars) is closer currently. 

As fainter and fainter stars are considered, the total number of stars grows quickly. The actual positions of these stars is more or less randomly distributed. So it's easy to see that exactly how close to the pole you can find a star is closely related to the faintest star you can see.