This is probably going to start getting on your nerves, but this termonology (I hope it's just the termonology) is killing me, and I think that you are not quite appreciating how much I am dying from it.
In my first post, I asked how to prove that d4x is a rank (0,0) tensor. (I am of course considering special relativity so the Minkowski metric tensor.) However, I see that you seem to be calling it a 4-form, which I understand to be a rank (0,4) tensor. Maybe I should say a rank (4,0) tensor. Anyway, I understand a 4-form to not be a rank (0,0) tensor.
Do you have any idea what is making me so confused? Am I just being incredibly stubborn about this? Is the distinction trivial or something?