CathInfo.com

There's also different kinds of papal doubts that Trads can have.  When one says "papal doubt" that does not mean only 1 thing.
1.  Spiritual Authority - All Trads implicitly doubt the spiritual authority claimed by V2 popes to do and say the unorthodox.
2.  Material Office - Being a Trad does not necessarily mean one doubts that a pope holds the material office.
3.  Spiritual Office - Being a Trad does not necessarily mean one doubts that a pope still has (in potential) spiritual authority.  Some say (i.e. Sedes) that his spiritual office is lost completely, once he utters heresy or abuses his spiritual authority (#1).  Others (i.e. Fr Chazal) say that his spiritual office is impounded due to material error, but could be regained by conversion.
.
The loss of spiritual authority seems to be agreed upon by all Trads.  #2 and #3 are debated.

Well, there are many permutations on this.  In my position, it's as a bit simpler:

MAJOR:  the Church cannot defect in her Mission
MINOR 1:  V2 and NOM present a wholesale destruction of faith and worship in the Church (followed by morals under Bergoglio)
MINOR 2: this degree of destruction would constitute the Church's defection from her Mission
CONCLUSION:  this degree of destruction could not have emanated from the legitimate authority of the Church.

As far as sede-this, sede-that, or sede-the-other-thing, the legitimacy of the Popes is by far a secondary matter that I'm not concerned about.  If someone wants to believe that Montini was replaced by a double, more power to them.  If you want to side with Bellarmine or with Cajetan, or come up with your own, it's all within the range of Catholic opinion only.  I don't really care.

MINOR 1 is generally what I hold to define whether someone is a Traditional Catholic and why I exclude the likes of XavierSem.  If you deny MINOR 1, then you need to make haste back to full communion with the V2 hierarchs.

MINOR 2 is in fact my major point of contention with modern R&R.  +Lefebvre agrees with this Minor, but some modern R&R don't.

In my position, it's as a bit simpler:

It's an over-simplification, which makes it difficult for everyone to accept.  Theology is often clearer, once you dive into the details.

If I were a priest, I would offer Mass “una cuм famulo tuo papa nostro” but then leave out the name, expressing sededoubtism.

Antichrist "Paul VI" loved the home made mass of Bugnini.