Bergoglio is a usurper of the Papal Throne
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Again, this is not a denial of his papacy. The term "usurper" doesn't necessarily mean someone who does not have the authority he claims. There are many instances in history of someone usurping a throne illegitimately, but becoming the actual ruler, such as through assassinating the current king or leading a revolution or something similar.
Saying Bergoglio is a usurper is not equivalent to being sedevacantist.