Cantarella, quoting Fr. Guerard said, "This permanence of the hierarchical structure constitutes the foundation while patiently awaiting the divine renovation of Authority; and it assures the material continuity of the hierarchical succession, a continuity absolutely required for the Church to retain her Apostolic Nature." It's amazing so many of those who believe in sedevacantism simpliciter don't even see the problem. At least Fr. Guerard sees the problem and attempts a solution.
Now, the proposed solution itself is unsatisfactory for a few reasons. First, because it is a novelty, the Church has never held traditionally that the power of jurisdiction itself is composed of matter and form; no, all theologians held and clearly taught that the power of order was the matter of the episcopate, which disposes a man to receive authority, while the power of jurisdiction was the form of Apostolic succession, by which he actually receives and exercise it. Matter and form are related as potency and act. A body as such is capable of being alive, but that it is actually alive, says St. Thomas, it owes to the vivifying principle of life that is the soul. The soul is the formal cause of life, while the body is the material cause. In a similar way, orders is the material cause of the episcopate, while jurisdiction is the formal cause. But is jurisdiction itself again subdivided into matter and form? Certainly, such a thing is not suggested by the canonists.
Some sedeprivationists will appeal to the Orthodox, saying they possess the material element of Apostolic succession but not the formal element. But this is because they possess the power of order, if they lost it, they would without doubt lose all connection whatsoever to the episcopate, just like the Protestants have. And yet most sedeprivationists believe the new rite to be invalid, so what exactly is the "matter" of the Papacy that Pope Francis possesses?
The second argument against sedeprivationism comes from the fact that the visible succession cannot be separated from the exercise of authority in the way Fr. Guerard proposes. For if it could, then what the Church has always argued against Protestants, schismatics etc is wrong. For the Church, all the Fathers, say that where the Apostolic succession, especially the principal or Petrine Succession in Rome, is continued uninterrupted from the time of the Apostles, there and there alone you will also find the Church. Consequently, if the church could be in one place and the material succession, even Petrine succession, in another, the Orthodox or any other group could also say, yes, the Apostolic and even Petrine succession is continued materially in Rome, but will become formal again only when Rome becomes (schismatic) "Orthodox". And this is clearly inadmissible. Therefore, such a separation is impossible, for it is precisely where the Apostolicity of the Church is found that the indefectibility of the Magisterium also resides.
As Brunsmann Preuss put it, "In order to be able to distinguish with certainty the true Church of Christ from all false claimants, it is sufficient to establish the Apostolic Succession with regard to the primacy of Peter ... Hence that Church, and that Church only, which can trace its rulers to the first primate, namely, St. Peter, is in fact and by right Apostolic in every sense." Note that here there is no suggestion that the true church can be elsewhere apart from the Petrine succession; for the visible line of succession itself is the infallible guarantee of where the true Apostolic, and therefore Catholic, Church is.
Third, while this statement "the material continuity of the hierarchical succession, a continuity absolutely required for the Church to retain her Apostolic Nature" is true, it is insufficient, a purely material continuity is not enough; as the Catholic Encyclopedia says, there must be in the hierarchy both the material and formal element of Apostolic succession. Hermann says, "Material succession consists in the fact that there have never been lacking persons who have continuously been substituted for the Apostles ; formal succession consists in the fact that these substituted persons truly enjoy authority derived from the Apostles and received from him who is able to communicate it. For someone to be made a successor of the Apostles and pastor of the Church, the power of order — which is always validly conferred by virtue of ordination — is not enough; the power of jurisdiction is also required, and this is conferred not by virtue of ordination but by virtue of a mission received from him to whom Christ has entrusted the supreme power over the universal Church."