Also, fwiw, this Formula was decreed over 1000 years before the Law of Quo Primum

Well it's not worth much, we already went over this.

I think very few people indeed (perhaps only you) would think that the words, "omit nothing" translates to,
"Always name whoever is touted as the legitimate Roman Pontiff at that time in the Te Igitur regardless of all circuмstances and evidence to the contrary."

Then those who did not continue to name Pius V in the Mass when he was dead would have "omitted something", and violated Quo Primum.

Then those who did not know Pius V had died and Gregory XIII had been elected and they continued to name Pius V in the Canon would have been "omitting" the name of the true Pope.

Obviously the "omit nothing" means "removing anything that the rubrics proscribe."

The rubrics proscribe naming the Roman Pontiff when alive.
If there is no Roman Pontiff at the time then that is to be OMITTED.
So, even according to your janky logic here, just following the rubrics in the case of sede vacante would be to violate Quo Primum! The rubrics call to "omit something"

I don't think any sane person would agree with you on this, but it is not essential to understanding the formula of Pope Hormisdas anyway.

The bottom line for me is this

Yes, yes, I know you are just looping back to Fr. Wathen as this is your default belief.

But will you confirm this is what the line from the formula means or not?

In other words, do you agree that the core principle is more broad and actually twofold?

i.e.

I promise that from now on those who are separated from the communion of the Catholic Church, that is, who are not in agreement with the Apostolic See, will not have
their names read during the sacred mysteries.

So the core principles would be more accurately stated thus,

"Only those who have the Catholic faith and acknowledge the legitimate spiritual authority over them should be named in that part of Mass because this naming symbolizes unity in the faith and eccelesastical subordination."

This is why the formula starts out with faith as supreme,

1) "The first condition of salvation is to keep the norm of the true faith and in no way to deviate from the established doctrine of the Fathers."

And then immediately expresses subordination,

2) "for in the Apostolic See the Catholic religion has always been kept unsullied. From this hope and faith we by no means desire to be separated."

It is only after these two principles are established that the formula goes on to pronounce the anathemas.

Yes, yes, I know you are just looping back to Fr. Wathen as this is your default belief.

But will you confirm this is what the line from the formula means or not?

You and gladius knock me for referencing Fr. Wathen in order to derail and imply he's wrong or something, but what you cannot do is dispute what he said, that's because what he said is truth.  

Of course I agree with it, when a good future pope comes out and condemns the conciliar popes to be heretics and schismatics and to omit their name from the canon, I will be 100% onboard. Why do you imply that I wouldn't? 

Now to your point about never excluding someone from the Canon (Pope or Ordinary),
Might there ever be any circuмstance and or doctrine that would not only allow, but oblige someone to omit a name from the Canon of the Mass? If yes, please elaborate.
Well, IDK maybe because your calling the teaching "crap" without telling us which teachings are "useless junk" - so it makes it look like you are disparaging the teaching because you would not specify WHICH teachings are false. This looks gravely suspect.

What are you reading? I never said the teaching was crap, I said the AI was crap . . .
"I don't know enough about it, but I know the AI link in the OP is full of crap and most certainly should not be used by those new to tradition." And that the AI is junk. . ."I don't know what you think you're accomplishing with this AI thing, but it's junk,"

So whenever you accuse me of saying something wrong, be sure you're accusing me of something I actually said.

The reason I said the AI was crap is because it describes heretics alright, but says the conciliar popes are not heretics. It says the pope's name can be omitted for heresy, and also says Quo Primum forbids it. The thing is unreliable, it's junk. It says V2 did not teach heresy. And there are other (easy) questions I asked it that are often brought up in debates here on CI, that AI's answers were 100% wrong.

Plus you performed a most impressive double entendre in claiming that you think the pope is a heretic and that he must still be named in the Canon.

1) You affirm the principle of non-communion with heretics/schismatics especially in omitting their names from the Canon.
2) But you then insist on a no-holds-barred interpretation of the the two words "omit nothing" from Quo Primum, which leads you to gaff and think heretics must always be named in the Mass until they are "officially declared by the pope" regardless of any circuмstantial or doctrinal consideration whatsoever.

I already posted why the priest prays for the pope by name in the canon, either you disagree with this excellent explanation, or you did not read it.

Here is another quote from Fr. Wathen - please show where he is wrong.

"....If the person who incurs the censure [of excommunication for heresy] be the pope himself, since there is no tribunal within the Church with the right to pass judgment against him, he cannot be removed from his office, even though he be under censure, and, according to the law, have no right to function as the head of the Church. We, his subjects, are not permitted to do anything about this. It is not within our right to declare his acts devoid of validity, due to his having been expelled from his office. Yes, the faithful may know well that he has committed a sin to which a censure is affixed by the Church, but this knowledge in no way qualifies them to declare him deprived of his office, or never to have been elected. We should have to continue to obey him as the pope in all those religious matters which fall within the ambit of his authority, UNLESS he should command something which is sinful."    

Yes, during a papal interregnum, which is the period of time between the death or resignation of a pope, and the election of the next pope. That is when his name is omitted, because he died or resigned.