There are three lines of argument that Bergoglio cannot be a true Pope:
Shortly before he died in 1226 A.D., St. Francis of Assisi prophesied that:
“A man, not canonically elected, will be raised to the pontificate… In those days Jesus Christ will send them not a true pastor, but a destroyer.”
In order to fulfill the prophecies of St. Francis and Daniel 11:21, only options 2 or 3 would apply. Option 2 ("pre-conclave lobbying) cannot be objectively proven, but is probably true. However, Option 3 (invalid election based on the issues around BXVI's renunciation), can be objectively proven.
But, the standard (Barnhardt/Bugnolo) take on the "invalid renunciation" is defective because it depends on a novel interpretation of the words of BXVI. They assume that BXVI did not, in fact, resign according to 1983 Canon 332. That is not objectively provable. Here is what BXVI said in his
Declaratio:
...with full freedom I declare that I renounce the ministry of Bishop of Rome, Successor of Saint Peter, entrusted to me by the Cardinals on 19 April 2005, in such a way, that as from 28 February 2013, at 20:00 hours, the See of Rome, the See of Saint Peter, will be vacant...
BXVI stated very clearly what he was doing. He resigned from his office as "Bishop of Rome" and the "See of Rome" will be vacant. Those quoted terms have specific meanings in Canon Law.
The mistake certain people are making is that they think that the "resignation" from the See of Rome (the Roman See) automatically causes a vacancy in the Apostolic See (the Holy See). That is incorrect.
The "Roman See" and the "Apostolic See" are two completely different entities according to Canon Law. The Roman See is set in St. John Lateran Cathedral. The Apostolic See is set in the Vatican. The Roman See is governed by the Bishop of Rome. The Apostolic See is governed by the Roman Pontiff (who is also the Bishop of Rome) and the Roman Curia together. The "Roman See" can be in a state of "vacancy" while the "Apostolic See" is not vacant. Note the differences in 1983 Canon Law:
Can. 335 When the Roman See is vacant or entirely impeded, nothing is to be altered in the governance of the universal Church; the special laws issued for these circuмstances, however, are to be observed.
Can. 359 When the Apostolic See is vacant, the college of cardinals possesses only that power in the Church which is attributed to it in special law.
If a vacancy in the "Roman See" is identical to a vacancy in the "Apostolic See," why are there substantially different restrictions on what is to be done. This is explained by the way that 1983 Canon Law defines the term "Apostolic See":
Can. 360 The Supreme Pontiff usually conducts the affairs of the universal Church through the Roman Curia which performs its function in his name and by his authority for the good and service of the churches. The Roman Curia consists of the Secretariat of State or the Papal Secretariat, the Council for the Public Affairs of the Church, congregations, tribunals, and other institutes; the constitution and competence of all these are defined in special law.
Can. 361 In this Code, the term Apostolic See or Holy See refers not only to the Roman Pontiff but also to the Secretariat of State, the Council for the Public Affairs of the Church, and other institutes of the Roman Curia, unless it is otherwise apparent from the nature of the matter or the context of the words.
So, the Apostolic See is a layered corporate entity, made up of and governed by many different people. But the Roman See is governed by a single person, the Bishop of Rome.
Now, we get to the papal election law
Universi Dominici Gregis, which clearly states that the election of the Roman Pontiff can take place only AFTER there is a vacancy in the "Apostolic See" (which is
not the same thing as a vacancy in the "Roman See"). As UDG 14 states, the vacancy in the "Apostolic See" only happen when the Pope dies:
14. According to the provisions of Article 6 of the Apostolic Constitution Pastor Bonus,13 at the death of the Pope all the heads of the Dicasteries of the Roman Curia — the Cardinal Secretary of State and the Cardinal Prefects, the Archbishop Presidents, together with the members of those Dicasteries — cease to exercise their office.
Therefore, even if the "Bishop of Rome" validly resigns, which BXVI did, the Apostolic See is not "vacant" until after "the death of the Pope."
Since a new election for the Roman Pontiff cannot take place until there is a vacancy in the "Apostolic See," and the Apostolic See was not vacant because BXVI was not dead in March of 2013, the election held in 2013 was illegitimate and completely null and void.
This thesis is the best one because everything needed to prove it is objectively available. There is no conjecture involved. One simply needs to read the law properly and to acknowledge that BXVI was not dead in 2013.