http://strobertbellarmine.net/books/Concerning_A_SSPX_Dossier_on_Sedevacantism.pdf

12. Having (incorrectly, I believe) explained the terms “public” and “notorious,” Fr. Boulet then applies them as follows.

3.5. Notoriety of law and notoriety of fact:

1. Notoriety of law: A crime becomes Notorious with a notoriety in law only when a judicial sentence has been rendered by a competent judge - but the Pope has no superiors and no one has juridical competence to judge him: “The first See can be judged by no one.”10 [www.sspx.ca]

- Hence any heretical act of John-Paul II cannot be Notorious with a notoriety of law.

2. Notoriety of fact: Can we say the same thing about the notoriety in fact of the Pope’s heresy? For it to be so, it would have to be widely recognised as both heretical and morally imputable – as Pertinacious (persistent and determined to the point of stubbornness). That is to say that it must be not only materially notorious, the heretical act being widely known, b but also formally notorious, the act being widely recognised as a morally imputable crime of formal heresy. We may see this from the comments of the canonists: “An offense is Notorious by notoriety of fact, if it is publicly known and committed under such circuмstances that it cannot be concealed by any subterfuge, nor excused by any excuse admitted in law, i.e., both the fact of the offense and the imputability or criminal liability must be publicly known.” [www.sspx.ca] So a papal act of heresy would be notorious in fact only if both the act were “publicly known” – and the “imputability or criminal liability” were “publicly known”. There is no competent judge who could rule of a Pope that guilt was involved, and so the guilt could be Notorious only by being widely publicly known – it would have to be widely known that the act was morally imputable. And it would be necessary that it could not be excused by an appeal to an “accident”, some sort of “self-defence”, or some other legally admissible excuse; it would also be necessary that “no subterfuge” could possibly conceal it.

a)   Against Fr. Boulet’s first point, in which he cites the divine law, The First See can be judged by no one, we may consider the Decretal Si papa, and the commentary upon it of Innocent III, who famously taught as follows.

He [the Roman Pontiff] can be judged by men, or rather can be shown to be already judged, if for example he should wither away into heresy; because he who does not believe is already judged.” (Sermo 4); see Decreta Gratiani, III, d. 40, c.6. 16 [Quoted by Mgr. G. Van Noort, Dogmatic Theology, Vol. II, "Christ's Church" - Mercier Press, 1958, p. 310.]

And the Decretal itself reads,

“Let no mortal being have the audacity to reprimand a Pope on account of his faults, for he whose duty it is to judge all men cannot be judged by anybody, unless he should be called to task for having deviated from the faith.” 17 [Ia, dist. XL, c. 6, Si papa; ex Gestis Bonifacii martyris.]

The Abbé de Nantes provides a parallel text from the same Roman Pontiff, as follows.

“The great Innocent III comments on this, applying it humbly to himself: ‘For me the faith is so necessary that, whereas for other sins my only judge is God, for the slightest sin committed in the matter of the faith I could be judged by the Church.’ (Serm. Consecrat. Pontif. Rom., P. L. CCXVII, col. 656).

Nothing turns on the point, but it appears to be inaccurate to say that no act of Paul VI’s, John Paul II’s, or Benedict XVI’s could be notorious with a notoriety of law, on the grounds that nobody may judge “the Pope.” For if any of the three were guilty of public heresy he would lose his papal status by the very fact, and could therefore be declared a heretic by an imperfect general council. This would render his heresy notorious with a notoriety of law.  

b) Fr. Boulet’s failure accurately to define the terms “notorious” and “pertinacious” now really causes some mischief. He avers that for heresy to be notorious “it would have to be widely recognised as both heretical and morally imputable,” which is simply wrong, as I hope has been demonstrated. There is no such requirement for “wide recognition” – although if it were widely recognised it would certainly be notorious. Likewise, Fr. Boulet informs us that, “guilt could be Notorious only by being widely publicly known.” Whence this novel term, widely publicly known?

c) Pertinacity also seems to cause some difficulties. Fr. Boulet tells us it means, “persistent and determined to the point of stubbornness.” But perhaps he has been deceived by an English dictionary, for that is the kind of definition he has given. Da Silveira himself has quoted several canonists on this point in his Essay on Heresy.

Moreover, it must be noted that the word "pertinacity" has, in the definition of heresy a different sense from that which it has in everyday usage. In the usual dictionary meaning, "pertinacious" means very tenacious, obstinate, secretive, persistent, continuing for a long time, perseverant. This is also the meaning of the Latin word.

If pertinacity, so understood, were essential to the sin of heresy, this would only exist in the cases of intrinsic malice which may be frequent, but is difficult to prove; it could only be determined after a long period of observation; it would never be committed in a moment of weakness, for example of anger.

Now the moralists and canonists are unanimous in affirming that the Code of Canon Law (can. 1325,D.2) does not use the term in this sense. As Tanquerey teaches, "pertinacity refers to denying or doubting a truth of the faith", "Scienter et volente", that is to say, with full knowledge that this truth is a dogma, and with full adhesion of will. "For there to be pertinacity", he adds, "it is not necessary that the person should be admonished several times and persevere for a long time in his obstinacy, but it is sufficient that consciously and willingly (sciens et volens) he refused a truth proposed in a sufficient manner, be it through pride or delight in contradiction or for any other reason." (Tanquerey, "Syn. Th. Mor. et Past.", pg.473.) Even if he denies it "brevi mora", ie. for a moment, a very brief space of time (Tanquerey, "Brevior Syn. Th. Mor.", pg.95) because pertinacity in this context "does not indicate duration of time, but perversity of reason" (Zalba, pg.28). There can be pertinacity in a sin of heresy committed by simple weakness (cf. Caietano in II; II, II.2.).

Concerning the canonical meaning of "pertinacity" in the definition of heresy, see also: St. Thomas "Summa Theol." II; II, II. 2,3; "Super Ep. ad Titum Lect.", n.l02; Wernz-Vidal, pgs. 449-450 Merkelbach, pg.569; Prummer, pg. 364; Noldin. vol. II, pg.25; Avis, pg. 292; Peinador, pg.99; Regatillo, pg. 142; Journet pg.709. [Arnaldo Xavier da Silveira, Essay on Heresy, translated by John S. Daly.]