Just think for a minute how events would have played out had there been a heretic Pope in the past ages of the Church when the majority of the hierarchy were clearly still Catholic.

1 ) Pope says something heretical.

2 ) Somebody close to him reprimands him.

3 ) Pope doubles down.  [If he retracted at this point, it's a non-issue.  So the heresy must in fact be pertinacious.]

4 ) More people reprimand and correct him.

5 ) Pope pertinaciously holds his opinion.

6 ) Growing doubt among more and more Catholics about his orthodoxy.

7 ) Universal Consensus that he's a heretic.

8 )  Church declares in Imperfect General Council that he's not the pope.

With Bergoglio we're on step 6.  At what point does the Papa Dubius situation kick in?  Somewhere between 3 and 6.  If during this time he were to define a dogma, what would the status of that dogma be?  Because of the serious positive doubt in play, it would not be possible to accept it with the absolute certainty of faith required of dogmas.  Thus the famous theological maxim:  Papa dubius papa nullus.:  a doubtful pope is no pope.  Meaning that, for all intents and purposes, due to the grave substantial positive doubt about his orthodoxy, he does not exercise teaching authority with the requisite certainty regarding its authenticity.  At that point he goes into the "quarantine" state described by Father Chazal.

Now, in the steps above, at what time does he cease to be Pope?  Well, I submit ... along with Father Chazal ... that he would formally cease to have authority somewhere between 3 and 6.

Now, when would Bellarmine say he was deposed?  Somewhere between 6 and 7 I imagine.  Many of the more dogmatic Bellarminist sedevacantists say 3.  But I find that problematic.  How about Cajetan?  Only at step 8, in his view, would the Pope cease to be pope.

Even then, what would be the status of any dogmas he tried to declare during steps 3-6?  That's in serious doubt.  This is why Bishop Guerard des Lauriers, in his thinking, significantly improved upon the state of this question.  If this Pope tried to define a dogma in the 3-6 stages, there would be positive doubt about its authority.  Consequently, for all intents and purposes, this Pope lacks all authority.  Again, Papa Dubius Papa Nullus.

So this is an incredibly complex topic.  And people are obviously entitled to have different opinions about it.

All I know, however, is that Vatican II and the Novus Ordo Mass could NOT have come from the legitimate authority of the Church.

Now, again, referring to the above steps, most R&R would follow the Cajetan opinion that he only ceases to be Pope at Step 8.  On its own a position that's defensible as Catholic.  That's why I have said that I have no issue PER SE with anyone who holds that opinion.  And I reject the calumny spread about me by Pax and Meg that I have declared heretical anyone who believes that the V2 Popes are legitimate.  I most certainly do not.  I reject only the proposition that an Ecuмenical Council and the Church's Universal Discipline (Rite of Mass and Canon Law) can become so corrupt as to endanger souls.  That I do consider to be heretical.  But if you wanted to say that Bergoglio is Pope based on following the Cajetan position and because Step 8 hasn't happened yet, that's your right to hold that.  But do NOT tell me that an Ecuмenical Council has taught heresy to the Church, or I will punch your lights out (virtually speaking, verbally, and by way of argument).  That's as if you would insult my mother calling her a whore.  Do not call my mother, Holy Mother Church, a whore ... I will NOT tolerate this.  That's why I will tear you to shreds for promoting that filth.  NOT because you happen to think that Bergoglio remains pope until deposed by the Church.

But the progression above shows why the Cajetan position is LOGICALLY untenable, and Bishop Guerard got it right.  Once there's positive doubt about a V2 Pope's orthodoxy, he cannot exercise authority with the REQUIRED certainty.  Everything he teaches and does and imposes becomes DOUBTFUL.  And, as such, there's no obligation to follow it.  Sededoubtism.  That's why Canon Lawyers have taught that someone is not schismatic if he refuses submission to a Pope based on grave positive doubts regarding his person or the legitimacy of his election.  I have BOTH.

And, finally, as I have said, very few R&R are actually TRUE sedeplenists.  To be a sedeplenist, you MUST accept the legitimacy of Bergoglio with the CERTAINTY OF FAITH.  You can no more speculative even hypothetically about the possibility that he MIGHT NOT be than you can speculate that there may not be Three Divine Persons in One God.  And every SSPX bishop has in fact thus speculated.  Once you speculated, this means GRAVE POSITIVE DOUBT regarding the Bergoglio (or his predecessors), and this means ZERO AUTHORITY, as Father Chazal has articulated.  I would guess that only 5% of all R&R are actually REAL SEDEPLENISTS.  Most of them just pay lip service to Bergoglio because he remains in material possession of the See and has not reached Step #8.  So much of the fighting on this matter is fake, and Sedeplenists are NOT IN FACT Sedeplenists but more Sedeprivationists (without admitting it).  Father Chazal has taken the step of properly articulating the reality of this position.

Cantarella believes that any 'joe plumber' catholic can make a determination on what is or isn't heresy, and also judge stubbornness too, of the Pope of all people, and do so 3,000 miles away from the comfort of their lazy-boy chair.  Talk about chaos!  Talk about "armchair" theologians!  This is insanity.

Cantarella believes that any 'joe plumber' catholic can make a determination on what is or isn't heresy, and also judge stubbornness too, of the Pope of all people, and do so 3,000 miles away from the comfort of their lazy-boy chair.  Talk about chaos!  Talk about "armchair" theologians!  This is insanity.

Yet, you have no problem with the same "joe plumber" recognizing heresy in nothing less that an Ecunemical Council and rejecting as sacrilegious a Rite of Mass promulgated and celebrated by the Sovereign Pontiff.

Ah, I see, so when a Pope dies and before a new one is elected, there are no Catholics left in the world ... since there's no Pope to be recognized.  And if I die during such an interregnum I would be lost, since I am not Catholic anymore.

The difference is that recognizing the pope as pope is REQUIRED to be catholic.

(but not to remain in Canonical submission to him nor to heed his Magisterium nor to worship God with the same Rite of Mass that he uses. 

There are significant numbers of clergy on both sides of the debate

I'm sorry but no traditional clergy have jurisdiction so they are not part of the hierarchy.  When I say 'hierarchy' i'm talking about Cardinals and officals of Rome, who have as their job the govermental aspects of the entire church.  No trad cleric has any say in the matter of the pope, because they don't have the power or vocation to 1) elect him or 2) study the theological questions surrounding his heretical actions.