I called DMV and court there. All are fact. I do have that ticket and I have paid fine. But they said it was a very minor negligent driving - anything can be this kind of charge including speeding, texting, etc. Also there is no way to remove the record in a legal way.
I just did not remember this when I filled out the application form. I guess if I answered "yes" and then explain, then it will be fine.
But now......
