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This is already the "4th Edition"  ... and I'm sure they haven't been keeping up.  They'd have to release a new one every week.

Getting back to Fr. Chazal's sede-impoundism for a moment. Of Course I don't agree with the impoundism, but I agree with Fr. Chazal when he said in his book, Contra Cekadam, that the sedevacantists let Francis get away. Why do they let him get away? Because, if Francis is not the Pope, and the conciliar church is not the church at all, then Francis gets away with his modernist heresy. It's only those who believe that he's still Pope, and that the conciliar church still has a semblance of Catholicism left that have hope and still try to work to change things. Sedevacantists have given up on Francis and the conciliar church. I won't do that. And I think a few other non-sedevacantists on this forum may agree with me.

We can determine that V2 popes are heretics.  Everyone in Tradition agrees with this, as V1 points out.  Where we must draw the line, is in making legal judgments and “throwing people out of office”.  As Fr Chazal points out, it’s sufficient to recognize the V2 popes as moral heretics.  Sedeprivationism says the same - their spiritual authority is gone. 

This is 90% of what’s important anyhow - the lack of spiritual authority.  Which all Trads agree on. 

Going further, and trying to unravel the temporal/govt aspects is nearly impossible.  I’ve never found out how it worked during Arianism and I’m not sure how it works now.  Only the future orthodox pope can fix this aspect. 

Throwing people out of office and making the temporal aspect of the office some “litmus test” of Traditionalism is a pointless waste of time, causes untold division, and solves nothing. 

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.