At this point, maybe it would be a good idea to step back for a second and reaffirm what is being discussed and what is not. Let's start with the following re-quote:
	
		
	
	
		
		
			
	
		
	
	
		
		
			Umm David, I was the one arguing that the phantom time shift didn't exist.
		
		
	 
	
		
	
	
		
		
			Well, that's pretty much what I've  been saying from the beginning........On the same waveform, a phase  shift is a time shift. Are you somehow suggesting that with a  single-phase, center-tapped, common-core transformer, you are getting  two different waveforms on the secondary from a single waveform on the  primary? When you change (ῳt) to (ῳt+180), it's either two waveforms or  an added time shift. Those two points do not occur at the same point on a  waveform.
		
		
	 
Your words from a few posts back.
		
 
		
	 
Apparently Besoeker and David Luchini took these comments to be contradictory with each other. So I will re-explain what these statements mean.
#1, I am asserting that a phase shift is a time shift. 
#2, I am asserting that because we know that you cannot have a time shift in a single phase transformer (as David has now affirmed regarding my non-symmetry example) then you cannot have a phase shift in a single phase transformer. Whether you agree or disagree with the assertions, is what is being discussed, but I have not wavered from them.
What's NOT being argued: Some people have a 
personal preference of designating the center-tap (neutral) as a common voltage reference. This is a personal preference, and as such, it 
cannot be argued. What may be leading to some needless confusion is that I suspect that some people might be asserting their personal preference as though it was mandatory for everyone to follow. 
Even though I do not make the choice to use the neutral as a common reference, I also do not try to force this choice on anyone else. That would be like trying to tell someone what their favorite color should be.
What IS being argued: Some people that choose the personal preference of using the neutral as a common voltage reference point have extended this choice to also mandate a 180? phase shift as part of their choice. Instead of acknowledging that their choice is just a polarity change, they are redefining the system to include a 180? phase shift that does not exist. 
It is technically correct to say that V
1n = -V
n1, but it is 
not technically correct to say that V
1n<0?= V
n1<180?. To say the latter introduces a time shift into the signal that does not exist.
Caveat: For the purposes of analysis, it can be acceptable to 
use V
1n<0?= V
n1<180?. However, where this steps over the line is when a person states that V
1n<0?= V
n1<180? is 
actual and 
real. My example of the non-symmetrical waveform proves that this condition is neither actual, nor real.