According to the setlist of the ill-fated 9/16 San Diego show, the track is called Not So Pretty Now, and once the setlist stats at The Art of Self Destruction go back online, I'll use it to tell you how many times it's been played this tour. It wasn't many.
Not long after it was played, 13 pages of discussion cropped up at ETS, including this attempt at transcribing the lyrics. And that's about the extent of what we know! Sorry for taking so long in reporting a new NIN song to you.