This is the symbol that represents the absence of a pope in the brief period during which a new pope is being elected. Sedevacantists for this reason are also called "conclavists" and adopt this as their official symbol.
Sedevacantism was one of the first issues that the Archangelati came into contact with, internally nonetheless. Sedevacantism is an anti-Catholic belief that the last several popes (the number varies) are not true popes due to their teachings being believed to be false and, in most cases, too modern. Most sedevacantists follow no Church leader though some have banded together and created a Pope of their own. The Archangelati accidentally accepted several of these into the group under the assumption that they were true Roman Catholics in communion with the Vatican but was led so falsely. Because of this and other similar problems, the new regulations for joining had to be established for the safety of the organization.