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Canon 2200.2, 1917 Code of Canon Law: “ When an external violation of the law has  been committed, malice is presumed in the external forum until the contrary is proven.

A commentary on this canon by Rev. Eric F. Mackenzie, A.M., S.T.L., J.C.L, states: “The very commission of any act which signifies heresy, e.g., the statement of some doctrine contrary or contradictory to a revealed and defined dogma, gives sufficient ground for juridical presumption of heretical depravity...  Excusing circuмstances have to be proved in the external forum, and  the burden of proof is on the person  whose action has given rise to the imputation of heresy. In the absence of such proof, all such excuses are presumed not to exist.”

St. Robert Bellarmine,  De Romano Pontifice, II, 30 :  “... for men are not bound, or able to read hearts; but when they see that someone is a heretic by his external works, they judge him to be a heretic pure and simple, and  condemn him as a heretic.

Again, you do not give ANY quotes regarding how to deal with a Pope who is in heresy. I specifically asked about Church teaching regarding how to deal with a Pope who is in heresy. When you provide the quotes I asked for, I'll respond to you further. 

That's between him and God. But there is such a thing as manifest heresy which clearly and explicitly contrary de fide teachings. Why is the ability to know this constantly questioned in general because many people don't possess the necessary faculties to discern it?
If my priest stands before the congregation and says:" I've converted to Islam", is his apostasy, in good conscience, not to be taken as an objective fact? If a bishop states publically that Jesus Christ did not come in the flesh and die on the cross, is there some reaosonable doubt left somewhere as to my obligation to shun him as a heretic? And if an apparent pope teaches moral relativism and gradualism as part of his authentic magisterium and, after being corrected, persists in this, what am I to think?

Yes, I've listed the different scenarios before:

1) "I am becoming a Buddhist."  --- ipso facto gone
2) "I know that the Church teaches x but I don't believe it anyway." --- ipso facto gone
3) "I believe x and don't consider it to be heresy." -- complicated

Ratzinger and Wojtyla certainly believed that they were being consistent with Tradition ... in applying their "hermeneutic of continuity".  But Bergoglio seems to know that he's breaking with Church teaching.  In the case of #3, the Church would have to discern that what he's saying is indeed heresy.  Then if he recanted, there would not have been any deposition ... even though the heresy had become "manifest".  If he then persisted, the "Church" could come back and reaffirm her judgment and warn Bergoglio that she would consider him a heretic if he persisted.  Then, after that, if he persisted, the Church could declare him deposed.  Undboutedly he would still have backers, and then what?  Call in someone to forcibly remove him from the Vatican when as a point of law the Pope owns Church property.  This would get messy very quickly.

Ultimately God will need to intervene and solve this mess.

In the meantime, there certainly exists grave positive doubt about their legitimacy.  And that's enough for me to refuse my submission without schism.