The definitions of phase and phase difference make no distinction between a delayed or advanced wave and an inverted wave.
I don't give a "rattus" what the mathematical definitions are....
I do not contend them! You can take that argument up with people foolish enough to follow it. I am not one of them.
When you take your mathematical transformation or representation and use it to redefine the system, that is when you are going to draw my attention....as has been stated countless times.
You don't have an answer for this contention that suits your needs, so you historically ignore it or trivialize it. In my opinion, this is extremely poor debating form. That is why I keep backing out of this discussion, because I refuse to engage in a debate where the information presented is not truly honest to the audience reading it.
You have stated that there is a physical phase shift that I contend is only mathematical. When I gave you a clear example where this is proven to be false, you chose to ignore it. I don't contend your mathematical representation, but stop telling people it is real.
The Inversion is REAL. The phase shift is Apparent!
Both of these concepts can exist peacefully next to each other, so long as you don't force one into the other. You are trying to shoehorn your apparent phase shift into a place where it is not absolute.
As I have said many times....this is NOT trivial, or you wouldn't be denying it and wouldn't keep repeating it.