It is good that you contrast the two elements that we need to consider:

Formal Pope = teaching/governing authority
Material Pope = physically holding onto the office

1983 Canon Law (1917 makes the same distinction using slightly different language):

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Can. 194

§1. The following are removed from an ecclesiastical office by the law itself [automatically]:
1/ a person who has lost the clerical state;
2/ a person who has publicly defected from the Catholic faith or from the communion of the Church;
3/ a cleric who has attempted marriage even if only civilly.

§2. The removal mentioned in nn. 2 and 3 can be enforced only if it is established by the declaration of a competent authority.

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So, the canon is clearly distinguishing between a de jure (formal) and a de facto (material) loss of office. The automatic/de jure/by-the-law-itself removal is what is referred to as the "formal Papacy." The declared/de facto/must-be-enforced-with-police removal is referred to as the "material Papacy."

A canonically-elected Pope loses his office (formally/de jure/by-the-law-itself) the moment he publicly defects from the Catholic Faith. No "declaration by a competent authority" is needed for anyone to recognize that fact and adjust their life accordingly. In that case, this canonically-elected Pope simply loses all of his authority and his dictates are binding on no one.

If that same canonically-elected Pope refuses to voluntarily vacate the physical office that he sits in, then his removal is only "enforced" by "the declaration of a competent authority." So a group of Cardinals would need to first recognize that 1) the former canonically-elected Pope has lost his office "formally." Then after that "formal loss" is acknowledged, those Cardinals can enforce the removal by calling in the Swiss Guard to physically kick the usurper to the curb.

P.S. Bergoglio is different from the papal claimants preceding him. He was not even canonically-elected, as you can read about at www.antipope.com. He was prophesied by St. Francis of Assisi: https://novusordowatch.org/saint-francis-assisi-prophecy-destroyer/. So none of the material/formal stuff is relevant to Bergoglio. He is simply a usurper and the Antichrist.

Your interpretations aren't binding on anyone. It's a matter of opinion.

Ladislaus, of all people, I wish you could see the value of distinctions and consistency.

The whole point of sedeprivationism, or Fr Chazal's impoundism is the same...which you often advocate...that the spiritual office is impacted immediately by heresy...but the temporal/govt office needs temporal/govt action by the hierarchy. 

OK, if that's what you mean, I have no problem with it.  At the same time, it wouldn't be schismatic for someone to have a different opinion, where the "spiritual" office (formal aspect of office) would also cause the evacuation of the temporal office.  I think some the terms are a little bit confused, especially when you equate the power to govern somehow with the material aspect of the office.  If by "governing" you mean the ability to make appointments, etc., then I don't disagree.  If by governing you mean something closer to jurisdiction or the power to command, then I would have to disagree.  Perhaps that's the root of the misunderstanding, terms.

I hold that a Pope formally deprived of office can make appointments, but has no power / authority to teach or to command.  This Pope could also serve as a conduit for jurisdiction.  Thus, if a heretical non-Pope appoints a bishop, and the bishop himself has no impediments to exercising the office, the bishop would have ordinary jurisdiction and could formally exercise the office.

OK, if that's what you mean, I have no problem with it.  At the same time, it wouldn't be schismatic for someone to have a different opinion, where the "spiritual" office (formal aspect of office) would also cause the evacuation of the temporal office.  I think some the terms are a little bit confused, especially when you equate the power to govern somehow with the material aspect of the office.  If by "governing" you mean the ability to make appointments, etc., then I don't disagree.  If by governing you mean something closer to jurisdiction or the power to command, then I would have to disagree.  Perhaps that's the root of the misunderstanding, terms.

I hold that a Pope formally deprived of office can make appointments, but has no power / authority to teach or to command.  This Pope could also serve as a conduit for jurisdiction.  Thus, if a heretical non-Pope appoints a bishop, and the bishop himself has no impediments to exercising the office, the bishop would have ordinary jurisdiction and could formally exercise the office.

Would you consider it heretical to say such a pope didn’t have authority to teach but that he still did have authority to command?  Why or why not?

We read these threads and ask the question of whether Francis is the pope, and whether we are able to judge the electoral process, the conclave, which elected him; and whether he, or other popes, were popes, and whether they lost offices through heresy, ad naseam.  My question is, How was John Paul not a valid pope?  He was elected by valid cardinals.  I have not "crunched the cardinals" so to say, but it is safe to say that most of the cardinals in 1978 were heretofore elected by valid popes, making them valid cardinals.  I know the Sede crowd will argue that many of the cardinals were created and appointed by Popes John and Paul VI.  But consider the Cardinal Siri Thesis for a moment:

Cardinal Siri died in 1989; John Paul II was elected in 1978. If Cardinal Siri was the validly elected pope, then the most we can say is that Card. Siri was cowardly for not defending his papacy in light of the usurpers trying to steal it from him.  How is there any other conclusion?  I know the contrarians will argue: "But hold on a minute Bryan, the enemies threatened to kill Siri and start World War III, blah blah."  So what!  Cardinal Siri was still a coward for not standing up and defending the papacy in the face of evil.  Those who promote the Siri thesis must prove us wrong, how is there any other conclusion?  I personally think the Siri thesis to be so laughable, almost beyond belief.  I am surprised that so many people hold it.   

So let me get this straight, from 1978-89 (during the reign of John Paul to the death of Siri) Abp Lefebvre is doing the best he can, flying around the world doing ordinations, et cetera...meanwhile Pope Siri the silent pope, let us call him "Siri the Silent," is apparently being a quiet, persecuted pope.  We hear nothing of him condemning the New Mass, nothing of him coming to the defense of Bp. Lefebvre, nothing of him defending his rightful claim to the papacy- all this in light of the fact that John Paul II is running around as a pretended pope.  If Siri was a valid pope, he was worse than these liberal popes, because he did nothing, absolutely nothing.  And why do we not hold Cardinal Siri to same standard as we hold all these traditional priests and religious who were thrown out of their houses by modernists?   

And it matters not one iota whether we be keyboard warriors or write lengthy tomes in defense of Christendom, the point remains, if Siri was pope, then he did nothing to defend the papacy; if he was not pope, then he still did nothing.  Why is that we all must accept the emotional argument that Siri was persecuted, so he therefore had a legitimate excuse to do nothing.  Cardinal Siri does not get a pass when it comes to God's justice, and he also does not get a pass from those faithful Catholics who must persist in this Great Apostasy.  And besides, I am not so sure that Siri was the orthodox champion his promoters make him out to be.  I have never read that Siri came out publicly against the New Mass; he never rallied any of those conservative bishops to his cause.  It appears that Siri was in the same camp as the majority of bishops and cardinals who went right along with Vatican II, a bunch of do-nothings.  As a matter of fact there is a picture on TIA's website of Cardinal Siri saying the New Mass ad populum. 


   

If Siri was elected at one of the conclaves, which there is evidence of, he definitely fell from the pontificate upon embracing the Novus Ordo religion.

A few pictures of Siri saying (what looks to be) the new mass is not enough evidence that he "embraced the novus ordo".  Heck, we even have pictures of St Padre Pio saying (what looks to be) the new mass.  But we know, by way of ample eyewitness accounts, that St Padre Pio DID NOT say the new mass, it was only 'ad populam'.  Context matters.  A picture is hardly proof; we need more.


I've basically heard that Siri was a prisoner at the Vatican.  Everywhere he went, he was followed.  I'm sure he wasn't allowed to write letters/give interviews, etc on the "changing landscape" of new-rome.  But, I admit, this Siri-apologizing also has limited evidence.  Was he a silenced prisoner, or was he was simply a fake conservative, coward who "went along with V2" to save his life. 

I don't think we'll know in this life.

I don't see how Siri could have had a chance of being pope, given that he did not accept being the Pope. One is not forced to be a pope if elected. If an elector refuses, as is his right, then he cannot be said to be pope.

According to the theory, though, he did accept.  Paul Williams (the former FBI consultant) indicated that he accepted and took the name Gregory XVII in the 1958 conclave.  Not only to you not take on a papal name, but also there's no white smoke send out unless and until the candidate has accepted.  As soon as someone accepts, he becomes the Pope.  Once he's the Pope, then, he cannot be forced to resign under duress (that would render the resignation invalid).

This is actually an act of diabolical genius.  See, these Mason/Communist/Jew operatives knew that a legitimately-elected Pope (even if he were an occult heretic, even a malicious infiltrator) would continue to be prevented by the Holy Spirit from damaging the Church this way, even if it meant that God would strike him dead.  That is precisely why they waited until Siri had been elected and accepted to come in with their threats.  They could have done so anytime before the conclave, told Siri up front that if he gets elected, he should refuse the election or else [whatever threats they had in play].  But to pull this off, they needed Siri to get elected and accept, in order to render the subsequent election illegitimate, so that the candidate was not the Pope and therefore not guided by the Holy Spirit (or at least prevented from teaching grave error to the Church).  It was a masterpiece of diabolical genius.

Masons actually thought they had their man on the See in Pope IX, but after Pius IX was elected, he had a conversion experience ... that came by way of an armed attack by the revolutionaries.  In fact, he was so liberal that a Cardinal was on the way to veto his election, but he was elected before he could get there.  From being a notorious liberal and welcome by all the same individuals who pulled off the Masonic revolutions in 1848, he turned into one of the most staunchly anti-"Modernist" (before St. Pius X had coined the term) Popes in history.

Sadly, these Illumaniti/Masons/Jews/Communists had more faith that the Holy Spirit would prevent a legitimate Pope from destroying the Church than R&R do.

There's actually some evidence that Pius IX was actually a Freemason before he was elected to the papacy, and he appears to have had a conversion experience ...

https://tinyurl.com/aj5z22e6