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This is what I was always taught...

Catholic Encyclopedia, 1911
Seems simple enough to me.    

I know we disagree on the sedevacantist issue , but I'm glad you're back and welcome!

The whole idea of Universal Peaceful Acceptance is that the identity of the pope is a dogmatic fact if he receives it. Well, maybe Francis *arguably* hasn't, but every other V2 pope certainly has. So if UPA is true then all those V2 popes were valid popes, utterly destroying the sedevacantist position.

You're begging the question.  You're falsely assuming that the other V2 papal claimants had UPA.  I disagree with that.

The whole idea of Universal Peaceful Acceptance is that the identity of the pope is a dogmatic fact if he receives it. Well, maybe Francis *arguably* hasn't, but every other V2 pope certainly has. So if UPA is true then all those V2 popes were valid popes, utterly destroying the sedevacantist position.

Yup. Also if the Papacy of His Holiness Pope Ven. Pius XII is not a priori known to be an infallibly certain dogmatic fact, neither could we know with absolute certainty, as we must, that the dogma of the Assumption defined by His Holiness is certainly true. In other words, if we could doubt his legitimacy, we could doubt the dogma. But it is heretical to say we can doubt a dogma. Hence, it must necessarily be true that the Papacy of a Universally Accepted Pope - such as all admit Pope Pius XII to be - is a dogmatic fact.

Further, it is proved by the indefectibility of the Ordinary and Universal Magisterium of the Church. For this reason, Pope Pius XII himself, in the dogmatic Bull declaring the dogma of the Assumption, says that the universal consensus of the Bishops, was already an infallible sign that the doctrine was true and definable. The principle of universal acceptance is same. Canonists and theologians say "universal acceptance is not the cause (the Pope being elected and accepting is the cause) but is a sign and infallible effect of a valid election". That is, if universal acceptance was present, it could only have been the effect of a certainly valid election being concluded.

One Caveat: I don't think any author, as far as I know, including St. Alphonsus, was speaking of the "second-man" scenario. As discussed. Thus, when St. Alphonsus says, "It is of no importance that in the past centuries some Pontiff was illegitimately elected or took possession of the Pontificate by fraud; it is enough that he was accepted afterward by the whole Church as Pope, since by such acceptance he would become the true Pontiff." this does not apply, I believe, when there is a sitting Pope already reigning whom someone else is opposing or trying to unseat. That's AFAIK, and it may be wrong, but that's what I think. But as far as appears, it does apply in every other case, for the reasons already mentioned.