CathInfo.com

Excerpted from this discussion, with the authorities relied upon for the opinion being St. Robert Bellarmine and Suarez:

http://www.cathinfo.com/catholic.php/Bellarmine-and-Suarez-on-The-Question-of-a-Heretical-Pope



Manifest Heresy

 in order for a person who has made materially heretical statements to be considered formally heretical in the external forum, pertinacity in the will would also have to be manifest. Obviously, if a Pope publicly defected from the Faith by leaving the Church, or by publicly admitting that he rejects a defined dogma, this, in and of itself, would suffice to demonstrate pertinacity in the external forum. But without such an open admission of guilt, there would have to be another way to demonstrate that he was manifestly obstinate in his position.

...

By remaining obstinate after two public warnings, issued by the proper authorities, the Pope would, as Fr. Ballerini said, pronounce sentence “upon himself”, thereby “making it clear that by his own will he had turned away and separated himself from the body of the Church” and, in a certain way, “abdicated the Pontificate”.

The bold is Siscoe's creation, what he quotes doesn't support it and neither does Ballerini support Siscoe's attempt not to prove sedevacantism FALSE, but to prove it unlawful or otherwise unapproachable.  You realize this, yes?  Siscoe's article never once touches on whether or not these men are popes, but focuses entirely on trying prove that we can't SAY they aren't, regardless of whether or not they are or aren't.  In other words, keep the truth to yourself :)

Admonitions are not necessary to determine that a heretic is manifest (history shows that even the Church does not always admonish before she condemns), and they certainly aren't restricted only to members of the hierarchy for them to be "valid" admonitions.  Ballerini himself says this.  Siscoe is an embarrassment to right-thinking.  His article is like a TV dinner, packaged up to sate the very specific needs of a very specific audience and prepared with no regard for the purpose of consumption.