Honestly, this thread needs to be put out of its misery and simply deleted.

A rite produced by a heretic (Montini) enjoys no presumption of validity, especially one that goes contrary to what a true pope taught is necessary for validity only a couple of decades prior.

So, indeed a Rite promulgated by a legitimate Pope would come with a guarantee (not merely presumption) of validity, but that's part of the question, isn't it?

If one held Montini to be a legitimate Pope, then what Pius XII said about the Prior Rite is not relevant, as all he did was take the existing Rite and settle a debate about what constituted the essential matter and form (since there was some debate among theologians).  Matter & Form in a different Rite altogether would not be the same.  So, for instance, had Montini been a legitimate Pope and he had merely adopted the Maronite Rite for use by the Roman Rite, the matter and essential form would obviously be different than what Pius XII had designated.  In other words, what he designated was not an absolute, but was specific the Prior Rite.

Now, he did lay down some principles within it such as that there had to be an invocation of the Holy Ghost and an unequivocal statement regarding the Sacramental effect of that invocation.  That's where the New Rite's removal of "ut" causes a serious problem, even though SSPX gaslight this issue with "it's only two letters", yeah, so is "is", and the word "not" are only 3 letters, but those words can make all the difference in th world.

"ut" means so that and precisely indicates that what comes after it was caused by what came before it, i.e. the cause (Holy Ghost coming down) leading to the (Sacramental) effect, making this man into a priest.  One might try to argue that it's implied, but that contention would be insufficient to dispel the very low bar of positive doubt.

But the bigger problem comes from Pope Leo XIII's Apostolicae Curae, in which he clearly laid out principles that even IF the essential form were corrected (Anglicans tried to desperately fix it), the history and intention of the Rite itself, as evidenced by removing all references to the priest's power to offer the Holy Sacrifice, to make them not contrary to the errors of the "reformers", had been vitiated, and the Rite was therefore irredeemable.  If you compare the Old and New, you see the very same thing going on, where there's a removal of all references to the priest being able to offer the Holy Sacrifice of the Mass ... where the Conciliars admit that their intention was the same, so as not to cause offense to the heretical views of the priesthood.  Now, I think there was a deeper sinister motive, a deliberate intention to destroy and to invalidate, but we needn't rely upon that, as their stated motives were already in line with what Pope Leo XIII had declared invalidated the Anglican Ordinal.

In the practical Order, howeve,r it's almost moot, since the Rite of Episcopal Consecration is almost certainly invalid, but easily show to be positively doubtful at the very least.

The armchair theologians have a new weapon...ChatGPT. No longer do they have to do any thinking or their own research and writing, all they need is a prompt for their AI engine and will publish the results as their own.

My goodness, I was reading through this thread wondering when someone was going to point out that this "forensic audit" was garbage that had been vomited out by AI. 

And yes, this entire explanation, as Ladislaus already said, is incoherent word salad. Practically all of the so-called terms distinctions in this text are specious and have nothing to do with scholastic theology. This guy really posted this nonsense and expects us all to think it's serious. Valor and validitas mean different things when discussing the sacraments? Are you serious? Have you ever read any manuals of sacramental theology? I gather you haven't because you would know that "ad valorem sacramenti" and "ad validitatem sacramenti" mean the same thing. Please take this stuff down, people read this website and are scandalised in their faith, all because people who don't know what they're talking about pontificate about the most important questions of our faith. 

And now AI is enabling these fools to generate more confusing garbage more amply.

Good grief.

My goodness, I was reading through this thread wondering when someone was going to point out that this "forensic audit" was garbage that had been vomited out by AI.

Well ... I didn't catch that it was AI, since the OP had created an equally nonsensical "monograph" concluding that the election of Bergoglio had been invalid due to a phrase in JP2's Universi Dominici Gregis which stipulated that the prior pope had to have had his funeral rites concluded prior to beginning the Conclave, and since Ratzinger had not died, the Conclave was illegitimate.  I pointed out in the Latin of UDG that it uses a subjunctive mood, with the notion that "funeral rites ... IF ANY", and that the docuмent speaks earlier of vacation of the office by death or resignation, which would be rendered nonsensical, since resignation would require that the See remain vacant until the resigned Pope had died and been buried.

But the OP here has continued to cling to that absurd conclusion for years now.

But thanks for also realizing the obvious reality that the random concatenation of various polysyllabic terms resulted in meaningless word salad and non-sensical non-arguments, where the words that he stuck together didn't even go together.

I was tempted to post this earlier, since it's rather fitting in response to the OP.  But until other people chimed in unsure of why it was nonsense, I didn't feel it was necessary to respond in any kind of detail.