I don't want to bore faithful long-time readers of my effusions ... but (happily) new readers do keep turning up. To these I desire to make clear that it is my policy to decline to enable posts which assert or imply Sedevacantism.
I have often written on this distasteful subject, and my pieces can, I presume, be accessed by means of the Search Engine.
Two very brief pointers.
(1) Sedevacantism is the other side of the same coin as Ultrapapalism (Hyperbergoglioism?) expressed by a number of the undesirables who surround the Holy Father. In each case, there is the same erroneous major premise.
The Pope is a reliable teacher of the Faith;
Bergoglio is clearly not a reliable teacher of the Faith;
Therefore Bergoglio is not pope.
The Pope is a reliable teacher of the Faith;
Bergoglio is pope;
Therefore Bergoglio must be a reliable teacher of the Faith.
BOTH ARE ERRORS.
(2) Whichever of the many forms of sedevacantism you are tempted by, subject it to the Pope Honorius Test. He was condemned by an Ecumenical Council and anathematised by a successor. But can anyone produce any evidence that the Council, or any subsequent popes who condemned him, or any reputable ecclesistical writer, has ever argued that Honorius had ceased to be Pope at the moment when he acted heretically?
Both the Council, and the Pope who confirmed the condemnation it decreed, anathematised him well after his death. They did not say that he fell from office during his lifetime.
Whether or not you like Bergoglio, he is, beyond any shadow of doubt, the Pope.