As a side note, one glaring issue I see with Fr. Chazal's position is that it goes against Vatican I, denies papal infallibility and bifurcates the papacy, separating the Pope from his Supreme authority. These same problems come up with Cassiciacuм (material-formal thesis) as well. If he is the legitimate Pope, then he has the full power of his office, he cannot be "impounded" as John of St. Thomas (an R&R favorite) taught nor can the office be merely "materially" occupied, but not formally, because to have one is to have the other. But I digress.
I disagree. Distinctions between different aspects of the papal authority are not "bifurcations". That's not what Vatican I was talking about. It was talking about the error of distinguishing between the person of the pope and his papal authority.
This distinction of the material vs. formal aspects of the papal office can be found in St. Robert Bellarmine.
One good illustration is this. Let's say a layman were elected pope, and he accepts. He has the designation to office but he cannot exercise aspects of that office. Not being a cleric, he cannot have jurisdiction over the the Church (e.g. tell bishops, priests, and other clerics what to do). So the next day he's ordained to the priesthood. That then allows him to exercise certain aspects of the papal authority, such as making appointments or other decisions. But he's still not fully pope at that point, since one must be a BISHOP. Nor can he exercise TEACHING authority, which is the most crucial aspect of the papacy, because only bishops are part of the
Ecclesia Docens (the teaching Church). Let's say this priest-pope refused to be consecrated a bishop. That would, according to theologians, constitute a tacit resignation from office, because the essence of the papacy requires being a bishop, and this would signal intent not to accept the papal office.
Papacy is absolutely unique in the Church. Bishops and priests all derive their authority from the pope. But the pope receives his authority directly from God. All the Church does is to DESIGNATE the person they have chosen to receive said authority, but their election does not formally imbue him with authority (whereas a papal appointment DOES imbue the bishops with their authority). So the election is the material aspect of the papacy, whereas the granting of authority in response to this election or designation by the Church is the FORMAL aspect of his authority. For bishops and lower, the two are inseparable. Bishops receive authority directly through their designation and selection by the Pope. But the papacy is the one office where the material aspect of election is clearly separate from the formal aspect of their receiving authority.