Questions for you:
(1) Who would that proper authority be? another Novus Ordo cleric who believes and professes the same Vatican 2 heresies as Francis? And if Francis is a valid pope and no one can make a private judgement that he has lost his office who is even allowed to judge a true and valid pope?
(2) What would Francis have to do or say that would lead you to believe he lost his office or at least probably lost his office? approving female priests? Approving ɧoɱosɛҳųαƖity? In other words, how far do your goal posts move?
Comment: I will give you credit for at least tackling Francis recent heretical antics. Most posters on this forum seem to be avoiding the main issue...either by not posting/ignoring it or attacking those that are not ignoring it and making no substantive, thoughtful comments.
I answered your first question in my last post while I was responding to Charlemagne.
My answer to your second question is that, generally speaking, a reigning Pope would have to resign or become deceased to lose his Papacy. If His Holiness Pope Emeritus Benedict XVI came out and stated that he was forced to resign, then I would be inclined to no longer accept the Papacy of His Holiness Pope Francis. A Pope can make heretical statements and still retain his Papacy if he is a material heretic.