No where did you prove that pertinacity must be established by the Church and only by the Church before a heretic is separated from the Church.  Instead, you directly oppose Pope Pius XII in Mystici Corporis where he states the sin of heresy by its nature separates one from the Church.  Here is the quote again:

“For not every sin, however grave it may be, is such as of its own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy.”
(Pope Pius XII, Mystici Corporis, 23) [Emphases mine]

CK: Proving that you have not understood the meaning of Popes Pius XII and Vigilius (for the reasons previously mentioned, namely, confounding the sin of heresy with the crime of heresy, and stemming from this, conflating the loss of membership in the Church with loss of jurisdiction and office), I'm hoping you will be receptive to the words of the eminent Cardinal Billuart and Pope Martin V:

Pope Martin V would be quite surprised to learn he stands condemned by Vigilius (Billuart as well)!

Summa S. Thomae of Charles Rene Billuart, O.P. (1685-1757)

Secunda Secundae, 4^th Dissertation: On the Vices Opposed to Faith.

~ Article 3 ~

"I say that manifest heretics, unless they are denounced by name, or themselves depart from the Church, retain their jurisdiction and validly absolve.  This is proved by the Bull of Martin V, Ad evitanda scandala, [which reads thus]:

"Then [the Bull] lists, as the only exception, those who are notorious for having inflicted violence on the clergy.  From these lines, we argue that the Church is granting permission to the faithful to receive the sacraments from heretics who have not yet been expressly denounced by name; and, therefore, that she allows the latter to retain their jurisdiction for the valid administration of the sacraments, since otherwise the concession granted to the faithful would mean nothing.

"Our argument is confirmed by the current praxis of the entire Church; for no one today ... avoids his pastor, even for the reception of the sacraments, as long as he is allowed to remain in his benefice, even if the man is, in the judgment of all or at least of the majority, a manifest Jansenist, and rebellious against the definitions of the Church; and so on with the rest.

"I have said in my thesis, 'unless they depart from the Church of their own accord'; for, by the fact that they depart from the Church, they renounce her jurisdiction, and as a result we infer that the Church does not continue to give it to them.  ...  If manifest heretics had to be avoided before their denunciation, this would endanger souls and generate anxiety of conscience, since there would be uncertainty as to who are manifest heretics, some persons affirming, and others denying, as actually happened in the case of Jansenism.  It is very difficult for lay people to know with certainty if someone is a manifest heretic or not, since in most cases the subject-matter of the heresy surpasses their understanding.  For all these reasons, the Council prudently decided that only those who have been denounced would have to be avoided.  These reasons, however, do not apply anymore once the heretic leaves the Church of his own accord.

"Nor does it follow from this—as if there were parity—that no one should be considered a public sinner unless denounced; or that, consequently, the Eucharist cannot be denied to any sinners except those who have been denounced.  The difference is, first of all, that the law and praxis of the Church require that a heretic be denounced before he loses his jurisdiction, not for his own benefit, but for the benefit and tranquility of the faithful.  But the Church does not require a denunciation for someone to be considered a public sinner, or to be repelled from Communion, because the welfare and tranquility of the faithful do not require that.  Also, it is not the business of the faithful to pass judgment on the jurisdiction of their ministers, and often it is impossible for them to do so; but this pertains to the superiors who grant the ministers their jurisdiction.  It pertains to the ministers, however, to pass judgment on those who receive the sacraments. ...

"The pope… does not have his jurisdiction from the Church, but from Christ.  Nowhere has it been declared that Christ would continue to give jurisdiction to a manifestly heretical Pope, since his heresy could become known to the Church, and the Church could provide another pastor for herself.  Nevertheless, the more common opinion (sententia communior) holds that Christ, by a special dispensation, for the common good and tranquility of the Church, will continue to give jurisdiction even to a manifestly heretical pope, until he has been declared a manifest heretic by the Church."

http://www.trueorfalsepope.com/p/thefollowing-excerpt-from-charles-rene.html

 

Sin is essential to crime, but crime is not essential to sin.  Crime needs sin, but sin does not need crime.  Therefore, every crime is a sin, but not every sin is a crime.  It follows, then, that the crime of heresy is contingent on the sin of heresy, but the sin of heresy is not contingent on the crime of heresy.  The crime of heresy exists only because it is defined as such by the Church in her Canon Law.  If the Church did not define heresy as a crime it would not exist as a crime, but the sin of heresy exists regardless.  Pertinacity in heresy is what is required to make the sin of heresy "formal" (i.e., a real offence against God).  Otherwise, the sin of heresy would only be “material” and hence not a real offence against God.  So what we have is that pertinacity is required for the sin of heresy and the sin of heresy is required for the crime of heresy.  Now since the sin of heresy exists with or without the crime of heresy and the crime of heresy need not exist at all, pertinacity essentially belongs, then, only to the sin of heresy.  But in her Canon Law, the Church does not judge pertinacity for the end of the sin of heresy but for the end of the crime of heresy.  The individual, however, may judge pertinacity, with the existence of sufficient evidence, for end of the sin of heresy.  And it is this sin of heresy that Pope Pius XII states in Mystici Corporis that, of its own nature, separates one from the Church.  And this is true regardless of the crime of heresy.     

CK: Proving that you have not understood the meaning of Popes Pius XII and Vigilius (for the reasons previously mentioned, namely, confounding the sin of heresy with the crime of heresy, and stemming from this, conflating the loss of membership in the Church with loss of jurisdiction and office), I'm hoping you will be receptive to the words of the eminent Cardinal Billuart and Pope Martin V:

Pope Martin V would be quite surprised to learn he stands condemned by Vigilius (Billuart as well)!

Summa S. Thomae of Charles Rene Billuart, O.P. (1685-1757)

Secunda Secundae, 4^th Dissertation: On the Vices Opposed to Faith.

~ Article 3 ~

"I say that manifest heretics, unless they are denounced by name, or themselves depart from the Church, retain their jurisdiction and validly absolve.  This is proved by the Bull of Martin V, Ad evitanda scandala, [which reads thus]:

"Then [the Bull] lists, as the only exception, those who are notorious for having inflicted violence on the clergy.  From these lines, we argue that the Church is granting permission to the faithful to receive the sacraments from heretics who have not yet been expressly denounced by name; and, therefore, that she allows the latter to retain their jurisdiction for the valid administration of the sacraments, since otherwise the concession granted to the faithful would mean nothing.

"Our argument is confirmed by the current praxis of the entire Church; for no one today ... avoids his pastor, even for the reception of the sacraments, as long as he is allowed to remain in his benefice, even if the man is, in the judgment of all or at least of the majority, a manifest Jansenist, and rebellious against the definitions of the Church; and so on with the rest.

"I have said in my thesis, 'unless they depart from the Church of their own accord'; for, by the fact that they depart from the Church, they renounce her jurisdiction, and as a result we infer that the Church does not continue to give it to them.  ...  If manifest heretics had to be avoided before their denunciation, this would endanger souls and generate anxiety of conscience, since there would be uncertainty as to who are manifest heretics, some persons affirming, and others denying, as actually happened in the case of Jansenism.  It is very difficult for lay people to know with certainty if someone is a manifest heretic or not, since in most cases the subject-matter of the heresy surpasses their understanding.  For all these reasons, the Council prudently decided that only those who have been denounced would have to be avoided.  These reasons, however, do not apply anymore once the heretic leaves the Church of his own accord.

"Nor does it follow from this—as if there were parity—that no one should be considered a public sinner unless denounced; or that, consequently, the Eucharist cannot be denied to any sinners except those who have been denounced.  The difference is, first of all, that the law and praxis of the Church require that a heretic be denounced before he loses his jurisdiction, not for his own benefit, but for the benefit and tranquility of the faithful.  But the Church does not require a denunciation for someone to be considered a public sinner, or to be repelled from Communion, because the welfare and tranquility of the faithful do not require that.  Also, it is not the business of the faithful to pass judgment on the jurisdiction of their ministers, and often it is impossible for them to do so; but this pertains to the superiors who grant the ministers their jurisdiction.  It pertains to the ministers, however, to pass judgment on those who receive the sacraments. ...

"The pope… does not have his jurisdiction from the Church, but from Christ.  Nowhere has it been declared that Christ would continue to give jurisdiction to a manifestly heretical Pope, since his heresy could become known to the Church, and the Church could provide another pastor for herself.  Nevertheless, the more common opinion (sententia communior) holds that Christ, by a special dispensation, for the common good and tranquility of the Church, will continue to give jurisdiction even to a manifestly heretical pope, until he has been declared a manifest heretic by the Church."

http://www.trueorfalsepope.com/p/thefollowing-excerpt-from-charles-rene.html

This quote deals with the jurisdiction necessary for valid administration of the Sacraments, which the Church regularly grants to non-Catholics ... not with ordinary or habitual jurisdiction.