Thanks to all who are coming in the discussion.
This topic is very important to understand in this unprecedented crisis we all suffer in, including atheists: "Is the Pope the Pope; a Formal heretic?".
It is certainly true that the present Pope (as with JPVII and JPII) are teaching modernism. I also realize in this "strike the shepherd; the sheep will scatter." situation, that in the consequence of this "scattering", there are now many more thoughts, understandings, groups, factions, and so on that had resulted in this crisis. Although we may not come to fully understand all that God may want in His providence to allow this to happen -except for the mystery of the cross- we do need to trust in Him to provide.
As this "broader conversation on sedevacantism and the SSPX" is developing, like any discussion, the basis of need to understand meaning and terms is essential. I believe we are coming to an understanding on this and ready to go to the core of the question: "Is the Pope the Pope; a Formal heretic?"
As RJS helped first to bring this to its next needed level, as with others who have helped to bring in the thoughts of the Holiness of the Church, there is a basic summation and premise that all of this "new level" is dealing with when we are talking about: "Is the Pope the Pope". Then after we can get to the next question of: is he a “Formal” heretic or not?.
To the first question: "Is the Pope the Pope". Let’s bring in an example:
A father of a family is a member of that family, first by natural propagation (let us leave that out to apply this example), he is a member by government and jurisdiction, and a member by the Faith in the "objective" sharing and cultivation of that faith commanded by God to spread that Faith.
One day, this father started, in his person, to "teach" something different to that Faith in the "supernatural life" in his private capacity while in the Chair of his position (like Aaron and the golden calf, Caiaphas condemning Jesus Christ to death, Solomon and his permission of ecuмenical groves to be built to false gods and worship, and many others who had "taught" things contrary to that Faith). The children members started to complain to their father about this. The father listened, or half listened, and continued on; perhaps in human respect, or in peer pressure, or in a different upbringing of “understanding” of that Faith in its meanings and terms, or an outright abandonment of that understanding of the Faith to purposely teach something else, as with many other possibilities (matter/material of the heresy).
As this persisted in the Providence of this cross in the family, God had provided also many prophecies and apparitions that this crisis will happen, there are now, unfortunately, more divisions and turmoils in the body of the family, which have now developed into different things of understandings, sayings, and beliefs from the original Faith and peace that was in that family to begin with. However, everyone does want the health of the body and membership of the family for the glory of God.
In this cross that continues for many years, there now comes a question in the family by some members: is the father still the father? The obvious to this question is: of course he is; he is the father. He is the father to still provide and govern the family. He still has the jurisdiction of authority to do so unless God removes him and replaces him with another (foster) father.
With this above example, it gives an understanding of today’s unprecedented crisis with speaking about the Pope. Like the father of the family, as with the Pope, the meaning and example is the same.
The Pope is “teaching” something different to that Faith in his private capacity of the "supernatural life", while in the Chair of his position, like Aaron and the golden calf, Caiaphas condemning Jesus Christ to death, Solomon and his permission of ecuмenical groves to be built to false gods and worship, and many others who had "taught" things contrary to that Faith, but they are still members of that governing capacity, with authority, and jurisdiction.
So is the Pope the Pope? Yes. He may have erred in his private capacity in the “supernatural life” like the father in his position; he is none the less, still the member of government, authority, and jurisdiction until God chooses to remove him.
I hope this helps to understand the meaning of the body of membership and what Archbishop Lefebvre had also stood up for in principle.
When others are ready, we can go to the next level of understanding the question of: is he a “Formal” heretic or not?
God bless.