TSA writes: "If you try to sign into PSN on your PS4, yo might find that you’ll be greeted with an error telling you that you cannot connect to the server and giving the error code NW-31201-7. Oddly, the PS3 and Vita seem unaffected."
PSN is back up for most. Those still having issues will likely have it back soon as the "update" works its way to you. Still some people claiming the store is not updated for them yet. Again, likely will come soon.