Pertinacity can be determined by one who does not have jurisdiction over the heretic in question.
False:
”St. Robert Bellarmine affirms that the loss of office (consequence of the crime) is based upon
the Church’s establishment of pertinacity (the crime) by virtue of ecclesiastical warnings. He says: “For in the first place, it is proven by authority and reason that a manifest heretic is ipso facto deposed [consequence under Divine law]. The authority is that of Blessed Paul, who in his Epistle to Titus, chapter 3, orders that the heretic be avoided after two warnings, that is after he clearly appears pertinacious [crime under Church law], and he understands (by this) before any excommunication and judicial sentence; as Jerome writes regarding this passage, where he states that other sinners are excluded from the Church through a sentence of excommunication, but heretics depart from and are cut off from the Body of Christ through themselves” [consequence under Divine law].
Note that Bellarmine affirms with Suarez and others under Divine law that “a manifest heretic is ipso facto deposed” as we have already seen. But he then says this conclusion is based on the “authority” of Titus 3:10, which requires warnings from ecclesiastical authority before the heresy is established and the heretic avoided (specifically, the authority that Titus, as a Bishop, had in his diocese). Then, “after two warnings” (when pertinacity is proved and the crime is established), Bellarmine refers again to consequence under Divine law (the heretic is “cut off from the Body”). Bellarmine’s language is clear, although sedevacantists attempt to deny what he actually said.
Suarez teaches the same regarding the crime (determined by the Church) and the consequence (dictated by Divine law): “I affirm: if he were a heretic and incorrigible, the Pope would cease to be Pope just when a sentence was passed against him for his crime, by the legitimate jurisdiction of the Church. This is the common opinion among the doctors.” Suarez also says: “Therefore on deposing a heretical Pope, the Church would not act as superior to him, but juridically, and by the consent of Christ, she would declare him a heretic [crime] and therefore unworthy of Pontifical honors; he would be then ipso facto and immediately be deposed by Christ [consequence], and once deposed he would become inferior and would be able to be punished” [human punishment].”1
http://trueorfalsepope.com/articles/salza/John%20Salza%20Responds%20to%20Another%20Sedevacantist.pdf