XavierSem never tires of recycling old arguments that have been addressed by sedes many times before.  He is blind.

Here's something new: http://www.strobertbellarmine.net/viewtopic.php?f=11&t=1845

And something that has been around for a while: https://romeward.com/articles/239749895/a-valid-papal-election-without-cardinals

An article on Sede-Vacantism in One Peter Five with the objection to sedevacantism now familiar to Cathinfo readers. With all the Bishops appointed by Pope Pius XII having passed, is the Catholic Church reduced to a non-Apostolic Church without a formally Apostolic Hierarchy and without any Ordinary Jurisdiction? The two objections (1) the Church can exist even without Ordinary Jurisdiction, and (2) can the "appointments" of a Heretical Anti-Pope confer authority? are considered. The first is precluded by the definition of formal Apostolicity, beside a statement in Vatican I. The second is excluded from cuм Ex - the one docuмent on a heretical Pontiff - and a statement by Fr. Gueranger that heretics without mission cannot appoint others to positions of authority.

From: https://onepeterfive.com/sedevacantists-church-without-pope/

Recently, an event of significance for sedevacantists came to pass. The last bishop consecrated to be appointed to office in 1958 — i.e., during the reign of Pope Pius XII — finally passed into eternity. That this is so can also be verified at the Catholic Hierarchy website and the updated lists at Wikipedia.

The most senior living bishop (sort the Wiki list by Consecrated Bishop) is now His Excellency Bishop Eloy Tato Losado of Spain. Consecrated bishop on July 25, 1960, about 60 years ago, during the reign of Pope John XXIII, this bishop was appointed to office and received his authority from that pope.

Why is all this of consequence for sedevacantists? Because many sedevacantists hold that Pope Pius XII was the last pope and that the See of St. Peter has been vacant since then, for almost 62 years.

Point I: Apostolic Succession Requires Ordinary Jurisdiction.

It is a common misconception that episcopal orders alone are sufficient for apostolic succession. In point of fact, both episcopal orders and ordinary jurisdiction (actual succession to an episcopal see) are necessary for apostolic succession. In the old manuals and theology books, the power of orders is sometimes referred to as the “matter” or material element of apostolic succession, while the power of jurisdiction is the form or formal element in a man’s succession to episcopal authority.[size={defaultattr}][font={defaultattr}]
Point II: Ordinary Jurisdiction Comes by Papal Appointment.

How does ordinary jurisdiction come to the bishops? The “last pope” of the sedevacantists, His Holiness Pope Pius XII, helpfully answers:
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Rev. Fr. Stanislaus Woywod, in his commentary on the Old Code of Canon Law, confirms:[/font][/size][size={defaultattr}][font={defaultattr}]
Point III: Ordinary Jurisdiction Cannot Cease in the Whole Church.

This is a logical consequence of the two points discussed above. It follows as a syllogism also:
Major: The Church cannot cease to be apostolic (as we profess in the Creed).
Minor: But ordinary jurisdiction is necessary for apostolicity (as proved above).
Conclusion: Hence, ordinary jurisdiction cannot cease in the whole Church.

As the Church of Christ cannot cease to be apostolic, so she cannot cease to have at least some bishops who are formal and full successors of the apostles. In this way, she retains the note of apostolicity as a permanent mark by which she can be distinguished from all breakaway sects.

Point IV: Therefore, the See of St. Peter Cannot Be Vacant Indefinitely.

This point follows from points 1 to 3. If ordinary jurisdiction and formal apostolicity can be transmitted only through the successors of St. Peter, and formal apostolicity cannot cease to exist in the whole Church, it necessarily follows that there must be perpetual successors of St. Peter until the end of time — as also defined dogma precisely says. The Petrine succession and the apostolic succession are intimately connected. Only a successor of St. Peter can “make” a successor to the apostles in the formal and full sense, by appointment to office conferring authority on him.

Point V: Therefore, it is heretical, and contrary to St. Peter’s perpetual successors, to hold to indefinite sedevacantism. It is necessary to renounce the error and to come out of it.

The Church cannot exist without the pope and without the powers he himself has communicated to others (like the bishops and cardinals) for the time of the vacant see.[/font][/size][size={defaultattr}][font={defaultattr}]
Thus, the Church cannot exist indefinitely once those bishops appointed by the last pope die. The Church exists only so long as the powers already communicated by the last pope remain.

An objection and its answer: “Does supplied jurisdiction save the day for sedevacantism?” No.

Not in the case of preserving apostolicity, for we have already seen ordinary jurisdiction (jurisdiction as a habitual power, as attached to a see or office) is necessary for formal apostolicity. Even an excommunicated priest may sometimes be supplied jurisdiction in a tacit and transient manner — however, this is not the equivalent of the Church conferring a permanent mission on him. The former does not equate to ordinary jurisdiction, but is only jurisdiction supplied for the act.

Supplied jurisdiction is referred to by canonists as a “delegatio a iure,” a delegation operative by the law itself. It is, basically, a tacit and transient delegation that comes from the Church — the Church here meaning the local bishop, the whole teaching Church, or the Roman pontiff himself.

So, even if jurisdiction is supplied to the sede bishops, that doesn’t make them successors to the apostles. Neither therefore does it preserve the apostolic indefectibility of the teaching Church.

Another objection: Would papal jurisdiction be supplied to the “heretic anti-pope (HAP) for his appointments?” Not so. For cuм Ex – the one docuмent on a heretical pontiff in Church history, which the earlier sedevacantists especially appealed to — explicitly says that those “appointed” by a heretic lack all authority. Those apparently “appointed” by heretics are not appointed at all [1].

Hence, if it is true that all the popes of the last 62 years have all been heretics, it necessarily follows that all their appointments are invalid, and the Church has defected and lost her formal apostolicity.
Conversely, if it is impossible that the Catholic Church defects and loses apostolicity, it follows that the popes doing the appointing to continue the succession must necessarily have been true popes.

Perhaps It Is Time to Come Home to Mother Church?

Sedevacantists deserve at least the same charity and courtesy shown to Protestants. Perhaps many sedevacantists are only in a material schism, earnestly not intending to be in schism.

But it is impossible to deny that sedevacantism, objectively and as such, constitutes a grave error. The simplest way to see this is to ask, “(1) How long can an interregnum last? (2) Is an interregnum indefinitely extended (e.g., 100-plus years) even possible?” Clearly not. There surely is a limit.

If saying an indefinite vacancy of St. Peter’s throne is possible, then the dogma that St. Peter must have perpetual successors in the primacy over the Church is a meaningless formula. Conversely, if that dogma actually means something, it means that the Church cannot be without popes forever.

Dom Prosper Guéranger writes how those who lost the Faith were unable to transmit the mission to others: “By God’s permission, the sees of Alexandria, Antioch, Constantinople, and Jerusalem, were defiled by heresy; they became chairs of pestilence; and having corrupted the faith they received from Rome, they could not transmit to others the mission they themselves had forfeited. Sad indeed was the ruin of such pillars as these! Peter’s hand had placed them in the Church. They had merited the love and veneration of men; but they fell; and their fall gave one more proof of the solidity of that edifice, which Christ Himself had built on Peter.”

Finally, sedevacantism really comes from a form of despair, fear, and worry that “it’s all over.”

Why should we worry when God is with us? Why should we despair when the Immaculata has promised us that, through the pope and bishops’ consecration of Russia, the Immaculate Heart will triumph, Russia will be converted, and a period of peace will be given to the world? How do we know that God may not act mightily in Pope Francis’s life? If we are Christians, we dare not say that that is impossible, but let us jointly pray, work, and sacrifice for that to come about. How do we know that God may not, after Pope Francis, give us a sovereign pontiff strong in the Catholic faith? To those who believe, all things are possible. If we pray, fast, work, and ask, the Lord will never fail us.

In conclusion, since sedevacantism is now known to be a harmful error, if any has adhered to it in the past, the time is now to come out of it and re-experience the glorious liberty of the children of God, by living in Catholic communion with the universal Church.[/font][/size]

[1] cuм Ex Apostolatus Officio: “[E]ach and all of their words, deeds, actions and enactments, howsoever made, and anything whatsoever to which these may give rise, shall be without force and shall grant no stability whatsoever nor any right to anyone[.]”

I haven’t read the article yet, but right off the bat, I would dispute there could be a Church devoid of ordinary jurisdiction or hierarchy.

I would have thought that much would be obvious, yet the sedes found a way to make an argument out of it.

What ordinary is the Resistance submitting to?  If you aren't submitting to an ordinary, how do you justify the necessity of an ordinary?

You used the word “submitting”! Get ready for Stubborn to chime in.....3....2....1

Can popes be resisted forever without undermining the necessity of the Petrine ministry?

Because many sedevacantists hold that Pope Pius XII was the last pope and that the See of St. Peter has been vacant since then, for almost 62 years.

How do some Roman rite trads justify not following Pius XII's directives, for example rejecting the revised Roman rite holy week?

You have no clue.

https://en.wikipedia.org/wiki/Canonical_situation_of_the_Society_of_Saint_Pius_X

That's the SSPX situation.  The Resistance situation is such that the pope you recognize doesn't even think you are Catholic.  Bishop Williamson is excommunicated.  You don't even have "partial communion" (whatever that means) with your pope.  Your recognition of him does nothing for you.  If he really is the pope, you aren't a member of the Catholic Church.  Your only hope is that Fr. Chazal is correct.

Not sure what you are talking about.

Do you know what you are talking about?

It would seem not.

Your premise is that a pope cannot excommunicate invalidly.

Yet the pope is not infallible in this regard.

And what does it matter what an heretical pope thinks about my Catholicity??

And most importantly, why are you prattling on about the Resistance, rather than explaining how there can be a church with ho hierarchy and no jurisdiction (the latter of which means there can never again be a hierarchy)???

Not sure what you are talking about.

Do you know what you are talking about?

It would seem not.

Your premise is that a pope cannot excommunicate invalidly.

Yet the pope is not infallible in this regard.

And what does it matter what an heretical pope thinks about my Catholicity??

And most importantly, why are you prattling on about the Resistance, rather than explaining how there can be a church with ho hierarchy and no jurisdiction (the latter of which means there can never again be a hierarchy)???

Obviously you don't know what you are talking about.  A hierarchy that can be resisted and overruled by the subjects is no hierarchy at all.  The Resistance view of ecclesiology may be compatible with Antifa doctrine but it isn't compatible with Catholic doctrine.

Effects of invalid or unjust excommunication

An excommunication is said to be null when it is invalid because of some intrinsic or essential defect, e.g. when the person inflicting it has no jurisdiction, when the motive of the excommunication is manifestly incorrect and inconsistent, or when the excommunication is essentially defective in form. Excommunication is said to be unjust when, though valid, it is wrongfully applied to a person really innocent but believed to be guilty. Here, of course, it is not a question of excommunication latæ sententiæ and in foro interno, but only of one imposed or declared by judicial sentence. It is admitted by all that a null excommunication produces no effect whatever, and may be ignored without sin (cap. ii, de const., in VI). But a case of unjust excommunication brings out in a much more general way the possibility of conflict between the forum internum and the forum externum, between legal justice and the real facts. In chapter xxviii, de sent. excomm. (Lib. V, tit. xxxix), Innocent III formally admits the possibility of this conflict. Some persons, he says, may be free in the eyes of God but bound in the eyes of the Church; vice versa, some may be free in the eyes of the Church but bound in the eyes of God: for God's judgment is based on the very truth itself, whereas that of the Church is based on arguments and presumptions which are sometimes erroneous. He concludes that the chain by which the sinner is bound in the sight of God is loosed by remission of the fault committed, whereas that which binds him in the sight of the Church is severed only by removal of the sentence. Consequently, a person unjustly excommunicated is in the same state as the justly excommunicated sinner who has repented and recovered the grace of God; he has not forfeited internal communion with the Church, and God can bestow upon him all necessary spiritual help. However, while seeking to prove his innocence, the censured person is meanwhile bound to obey legitimate authority and to behave as one under the ban of excommunication, until he is rehabilitated or absolved. Such a case seems practically impossible nowadays.

Bishop Williamson and the Resistance if they have been unjustly excommunicated by a true pope are "bound to obey legitimate authority and to behave as one under the ban of excommunication, until he is rehabilitated or absolved."  Fr Chazal doesn't worry about that because he doesn't think Frank is a true pope in the sense that he legitimately holds the office of the Bishop of Rome.  Fr Chazal believes that Frank has no authority in the Church.  But you think that Frank does hold authority in the Church but that you can overrule him if you judge his discipline doesn't measure up to your standards.  That's not a Catholic hierarchy.  A true pope can even suppress a religious order that was not guilty of any crimes (e.g. Society of Jesus in the 1700s).  Some people might consider that unjust but the pope has the authority to do it.  And we would be bound by his decision.  So spare me your patronizing attitude about the hierarchy.  At least sedes have the hope of an election.  Whereas R&R will be stuck in the Novus Ordo until the end of time.