I've read a number of posts by those claiming the SSPX lied during the consecration of the bishops by claiming the papal mandate. But, in the course of the consecration Mass, when asked if they had the papal mandate, Bishop Fellay did not say "Habemus," (We have it.) Instead he called on the notary, Fr. Foucauld Le Roux, to read a declaration of necessity which implicitly recognized the lack of the papal mandate. The sedevacantist site, Novus Ordo Watch, where I found the text of the document, says this indicates that the SSPX recognizes Leo as a legitimate pope and are living a contradiction by acknowledging the conciliar church but refusing to obey its pope. Hmm....