IPad Air 2 (cellular) upgrade to 9.3.1 won't run (after "agreeing", takes me to home screen)
Installing via iTunes works (i.e., plug iPad into computer with iTunes running), so I ended up doing that.  

For others that run into this problem: you may want to make sure you have enough disk space on your device. I had 32gb, so I know that wasn't my problem.  

I suspect my problem had something to do with the 9.3 update arriving, and then Apple unsigning it because of its bugs; and maybe when 9.3.1 came out, my iPad was confused?  shrugs