Padre Pio and Chiesa viva
The followers of the Siri Thesis claim that during the papal conclave of 1958, Cardinal Siri, who was considered the leading conservative candidate, was elected Pope on the first day of the conclave, October 26, and took the pontifical name of Gregory XVII. However, the pro-Siri movement itself quoted Siri as making clear his intention to refuse if elected. 
Newspapers the world over carried the Associated Press picture of the white smoke emanating from the Sistine Chapel chimney from 5:55 PM until 6:00 PM on October 26, 1958. White smoke indicates that a Pope has been elected. Vatican Radio also concluded that a Pope had been elected on the third ballot and announced it as such, telling listeners, "The smoke is white... There is absolutely no doubt. A Pope has been elected." However, no Pope appeared, and at 6 PM the smoke changed to black, signaling that no Pope had been elected.
Two days later, the white smoke again rose from the Sistine Chapel, and Angelo Roncalli emerged to become Pope John XXIII. Supporters of the Siri Thesis believe that evidence indicates that Cardinal Siri was elected on October 26 when the white smoke was seen but no Pope emerged on the balcony, and that dire threats against the Cardinals and the Vatican were made during this time, emanating in part from the Kremlin. Some[who?] believe that the pressures included a nuclear threat against the Vatican itself if Siri were not set aside and a more acceptable candidate chosen.
This idea is founded on the outcry against Siri's strong anti-communist stance.
Malachi Martin later said that Siri had been elected as Pope during the Papal conclave, October 1978. He said in March 1997 on Paranet Continuum radio programme Steel on Steel, hosted by John Loefller, that Siri had received a written note after his initial election threatening him and his family with death should he accept. Martin wrote of threats which involved "the very existence of the Vatican state" during a conclave on pages 600–10 of his book The Keys of this Blood. According to Martin, after such threats entered the conclave, progressive factions amongst the cardinals in the conclave, particularly the French cardinals, pressured Siri to step aside, claiming that his strong anti-Communistpolicies would lead, among other things, to widespread persecution of Catholics in Eastern Europe. Siri would then have accepted this suggestion and stepped aside, rather than having said that he would refuse to serve if elected.
The United States Federal Bureau of Investigation allegedly claimed that Siri had indeed been elected on the third ballot on October 26, 1958, according to the book The Vatican Exposed: Money, Murder, and the Mafia by Paul L. Williams on pages 90–92, which cites an FBI document as reference; this document, allegedly declassified, can no longer be found; Williams adamantly refused to comment on why he included the alleged document and reference number in his book, or why the document could no longer be viewed.
According to some Siri theorists, if Siri had resigned, it would have been invalid according to Canon 185 of the 1917 Code of Canon Law, which states (Canon 188 in the 1983Code of Canon Law): "Resignation made out of grave fear that is inflicted unjustly or out of malice, substantial error, or simony is invalid by the law itself." Additionally, decades earlier Pope Leo XIII proclaimed: "When all that we have thus far described has been done [the precise laws of a conclave have been followed], he who is elected is Pope, in all right and justice, and no man can in any way call his election in question or endeavor to invalidate it. He governs the Church from that moment, and no other act is required to give him further authority. Some, it is true, assert that the coronation is in some way necessary to the perfection of the election. However, this ceremony is by no means essential, for we find that Clement V threatens with excommunication those who assert that bulls issued before the coronation are not binding."