Quote I think everyone agrees with this
Actually, they don't. The schismatic Ladislaus has claimed he has a right to refuse Cardinal Billot's teaching that unanimous acceptance provides a sanatio in radice of an unanimously accepted candidate. So it's just a lip service he gives, but when really pressed, is forced to acknowledge he disagrees with the teaching itself, owing to various absurd rationalizations.
But supposing you accept the teaching, but claim you deny it applies today - then you are on par with someone who denies the Catholic Church teaches the dogma of the Assumption. For that was unanimously accepted, and it is a fact so unanimously known that the world acknowledges it - just as the whole world knows and acknowledges that Pope Francis and his 5 predecessors have been the Popes and Heads of the institution known as the Roman Catholic Church. Now, if you've read Fr. Hunter, and agree with him also, that if the Bishops recognize the Pope, he is the Pope, hear Pope Benedict XIV on the subject:
"
it suffices Us to be able to state that a commemoration of the supreme pontiff and prayers offered for him during the sacrifice of the Mass is considered, and really is, an affirmative indication which recognizes him as the head of the Church, the vicar of Christ, and the successor of blessed Peter, and is the profession of a mind and will which firmly espouses Catholic unity. This was rightly noticed by Christianus Lupus in his work on the Councils: “This commemoration is the chief and most glorious form of communion” (tome 4, p. 422, Brussels edition). This view is not merely approved by the authority of Ivo of Flaviniaca who writes:
“Whosoever does not pronounce the name of the Apostolic one in the canon for whatever reason should realize that he
is separated from the communion of the whole world” (Chronicle, p. 228); or by the authority of the famous Alcuin: “It is generally agreed that
those who do not for any reason recall the memory of the Apostolic pontiff in the course of the sacred mysteries according to custom
are, as the blessed Pelagius teaches, separated from the communion of the entire world” (de Divinis Officiis, bk. 1, chap. 12).
Pope Pelagius II who held the Apostolic See in the sixth century of the Church gives this weightier statement on Our present subject in his letter: “I am greatly astonished at your separation from the rest of the Church and I cannot equably endure it. For Augustine, mindful that the Lord established the foundation of the Church on the Apostolic sees, says that whosoever removes himself from the authority and communion of the prelates of those sees is in schism.
He states plainly that there is no church apart from one which is firmly established on the pontifical bases of the Apostolic sees. Thus how can you believe that you are not separated from the communion of the whole world if you do not commemorate my name during the sacred mysteries, according to custom?
For you see that the strength of the Apostolic See resides in me, despite my unworthiness, through episcopal succession at the present time” (Labbe, Conciliorum Collectione, vol. 5, col. 794f and 810)."
https://www.papalencyclicals.net/ben14/b14exquo.htm Therefore, when anybody drops the name of the Pope from the Canon who is recognized by the whole world as Pope, he is schismatic.
Major Premise: The Bishops of the world recognize the Pope (in the way Pope Benedict XIV says; this is proved from Ex Quo)
Minor Premise: If the Bishops of the world recognize the Pope, then he is certainly Pope (as per Fr. Hunter, Fr. Connell, Van Noort etc).
Conclusion: Therefore, the Pope is certainly the Pope. And the last six Popes have certainly been Popes. And to fail to recognize this is schismatic (and damnatory, for as Pope Boniface teaches, "we declare, we proclaim, we define that it is absolutely necessary for salvation that every human creature be subject to the Roman Pontiff.")
http://www.newadvent.org/library/docs_bo08us.htmCorollary: Any schismatic, like Ladislaus, (also proved from Eighth Ecuмenical Council, and from Ex Quo above) is excommunicated and schismatic, if he "does not pronounce the name of the Apostolic one in the canon for whatever reason" or defends doing so.
Be wise and do what is necessary to save your souls. Because, in the Name of God I announce to you, out of Love and Charity for your souls, that you cannot save your souls in 62 year sedevacantism. I do you no favors by hiding this Truth from you. The rest is up to you, and your correspondence with God's Grace, given to you for the purpose of your humbly returning to the Catholic Church, by recognizing all Her Popes, who have been recognized by the Episcopate.
Like this woman wrote in the Remnant, it is best for svists and evists to face the facts now, and the clear Truth, after 62 years at last: "They told me what was necessary for salvation because I was their friend ... I just needed to be Catholic."
https://remnantnewspaper.com/web/index.php/articles/item/3931-where-have-all-the-catholics-gone You will certainly have to recognize the Popes recognized by the Magisterium before having to go to Heaven.