Fair enough.

What do you make of Bellarmine's argument against the 4th opinion?

"before excommunication and sentence of a judge."

Your argument, if it makes any sense at all, is that the claimant is the true pope with supreme authority until the moment a discretionary judgment is made against him.  If that's not the case, then you have no argument with sedes and your entire book is a fraud.  The fact that none of us here understand your slippery arguments is prima facie evidence that you are dishonest liar.  No one understands it because it sucks.  You are a meathead who wasted 15 years of your life studying a topic without ever conforming yourself to the doctrines of the theologians you were reading.  Instead you picked through it and cobbled together a twisted theory that cannot be found in any theology book anywhere.  Did the Novus Ordo people discover your theory when they decided that Frank had gone too far?  No, they came to the same exact conclusion as the sedes.  Does Cardinal Burke agree with you? No.  Does Ed Peters agree with you? No.  You and your buddy are losers who are trying to prop up the failed R&R position.

Your argument, if it makes any sense at all, is that the claimant is the true pope with supreme authority until the moment a discretionary judgment is made against him.

The fact that none of us here understand your slippery arguments is prima facie evidence that you are dishonest liar.  No one understands it because it sucks. ...  Does Ed Peters agree with you? No.  

Father Ghirlanda, S.J., (2013):  “The vacancy of the Roman See occurs in case of the cessation of the office on the part of the Roman Pontiff, which happens for four reasons: 1) Death, 2) Sure and perpetual insanity or complete mental infirmity; 3) Notorious apostasy, heresy, schism; 4) Resignation.  In the first case, the Apostolic See is vacant from the moment of death of the Roman Pontiff; in the second and in the third from the moment of the declaration on the part of the cardinals; in the fourth from the moment of the renunciation." (…) There is the case, admitted by doctrine, of notorious apostasy, heresy and schism, into which the Roman Pontiff could fall, but as a ‘private doctor,’ that does not demand the assent of the faithful (…) However, in such cases, because ‘the first see is judged by no one’ (Canon 1404) no one could depose the Roman Pontiff, but only a declaration of the fact would be had, which would have to be done by the Cardinals, at least of those present in Rome.” (La Civiltà Cattolica, March 2,  2013)

    Although the opinion that a public heretic would lose office entirely by himself, ipso jure divino (i.e. ipso facto), was already formulated by canonists in the twelfth century, Salza & Sisco dismiss it as "sedevacantist theology" -- as if it were a modern sedevacantist invention. How can it be possible that such theologians as Cajetan, John of St. Thomas, and Bordoni were aware of that opinion and argued against it; but if the Salza/Siscoe interpretation of Bellarmine's fifth opinion were correct, then Bellarmine would have been ignorant of the opinion asserting an ipso jure divino loss of office for a pope who becomes a public heretic. It is inconceivable that Bellarmine could have been ignorant of that opinion, and that he would not have listed it as one of the opinions on the question of deposing a heretic pope. Hinscius (1869) mentions that a whole series of authors favour that opinion of an automatic forfiture of office by a manifest heretic pope. Gregory XVI interprets the Bellarminian opinion as formulated by Ballerini in the same manner, i.e., that the manifest heretic pope would lose office "by himself", having "abdicated" the pontificate by his pertinacity; and that the judgment of the Church would be made not against the pope antecedently, but against him "who before was adorned with papal dignity." According to Salza & Siscoe, the fifth opinion calls for an antecedent judgment by the Church; which means Gregory XVI and the entire series of authors mentioned by Hinscius understood it wrongly -- and it would mean that Bellarmine himself was ignorant of that opinion formulated by canonists since the twelfth century. Historically there have been five opinions. The first opinion is that the pope cannot be a heretic. The second is that all heretics, even secret heretics, lose office ipso jure divino (ipso facto). The third is that a manifest heretic pope is not deposed ipso facto, nor can he be deposed by the Church. The fourth is that a manifest heretic is not deposed ipso facto, but must be judged and deposed by the Church. The fifth historic opinion is that the public heretic falls from office entirely by himself, ipso facto, before any deposition or trial. Deposition is a threefold act, (as Bordoni explains), comprised of 1) judgment, 2) deposition, 3) penal sanction. Historically, the fifth opinion asserted an ipso jure divino loss of office without any antecedent judgment or declaration. This opinion was opposed by Cajetan, John of St. Thomas, Suárez, Bordoni, and many others. According to the Salza & Siscoe theory, this historic opinion of an ipso jure divino loss of office for public heresy without an antecedent judgment is not one of the historic five opinions, but a sedevacantist misintetpretation of Bellarmine! The Salza/Siscoe interpretation of the fifth opinion is straight out of the lunatic asylum. Against the teaching of the expert canonists who list Suárez as holding opinion no. 4, Salza & Siscoe claim that Bellarmine and Suárez were of the same opinion, i.e., no. 5! Fr. Jean-Michel Gleize accurately described the Surezian opinion as a logically incoherent synthesis of opinions no. 4 and 5. Suárez's opinion is not the historic no. 5 as Salza & Siscoe ignorantly claim.

This^^^^ is the emotional outburst of someone desperate to salvage his position, because he is aware he is being destroyed in the debate.

At the end of the day, people can hold any number of positions on this subject provided that they do not violate Catholic teaching.

If in fact, the Magisterium and Universal Discipline of the Church had not become corrupt, then this would be an entirely academic question.  If the Magisterium were intact and the Tridentine Mass were being offered, if Bergoglio was running around saying heretical things, it has no impact on me, and I would just write it off as "not my problem".

But we have a problem.  If Vatican II and the New Mass are from the legitimate Pope, then I'm accepting them ... as should all Catholics ... without any fear of our displeasing God by doing so.

Are you capable of getting anything right?

Of course the ipso facto loss of office without an antecedent judgement is one of the Fiive Opinions.  It's the 2nd Opinion, which Bellarmine refutes and which you defend.  

Now, to anticipate you're objection, you believe a Pope cannot fall into heresy (1st Opinion), but you also say if he did he would fall from the Pontificate even if his heresy was committed entirely in secret, by an interior act alone (2nd Opinion).