Best of wishes to you all, you may have just incriminated yourself if you got the unable to authenticate error however. Seeing as PokemonGo has had nothing but login server issues for 3 weeks straight, jumping to an appeal letter before waiting for those to be fixed, may have just incriminated you (simply put: if you weren't botting you shouldnt assume you have to appeal a ban):
I received the “Unable to authenticate” or “Failed to log in” message – Pokemon GO even Niantic makes it clear that this error pops up in these occasions. Next time consider playing it dumb and just sending in a trouble ticket saying you are having login issues.... Makes you look alot less guilty