What is meant by being pope materialiter?

The main difficulty of sedevacantism is to explain how the Church can continue to exist in a visible manner (for she has received from the Lord the promise that she will endure until the end of the world) while being deprived of her head. The partisans of the so-called "Cassiciacum Thesis"[2] have come up with a very subtle solution: the current pope was validly designated as pope, but he did not receive the papal authority because there was an interior obstacle (heresy). So, according to the theory, he is able to act in some ways for the good of the Church, such as, for instance, appointing cardinals (who are cardinals materialiter), but he is not really pope.

What do you think of this solution?

For one thing, this solution is not based on Tradition. Theologians (Cajetan, St. Robert Bellarmine, John of St. Thomas, etc.) who have examined the possibility of a heretical pope, but no one prior to the Council every devised such a theory. Also, it does not resolve the main difficulty of sedevacantism, namely, how the Church can continue to be visible, for, if the pope, the cardinals, the bishops, etc., are deprived of their "form," then no visible Church hierarchy is left. Moreover, this theory has some serious philosophical defects because it supposes that a head can be head materialiter, that is, without authority.