Papal Mainframe

The Papal Mainframe was a space church, led by the Mother Superious Tasha Lem, leader of the Church. It had its own military force and weaponry. One of the Papal Mainframe's customs was that visitors to the church would have to arrive without clothing, or at least it was appreciated to do so. Holographic clothes were acceptable, however all employees of the Papal Mainframe were trained to see through these.

When a mysterious message that filled the higher species with fear spread to every corner of space and time, the Papal Mainframe was the first ship to arrive at Trenzalore, the source of the message, and shielded it so that nobody could land. However, unknown to the church, the Weeping Angels had already arrived on planet.

Tasha Lem at some point summoned the Eleventh Doctor and Clara Oswald to the Mainframe in response to the message. Feigning ignorance as to its contents, she sent them down to the planet to discover the truth themselves.

After she discovered that the message was the First Question, sent by the Time Lords from their pocket universe, Tasha Lem communicated to the Doctor that if he took action to save the Time Lords, he would cause the fleets above to destroy them. The Doctor refused to allow The Mainframe to destroy the planet and spent the next 300 years defending it. The Papal Mainframe also busied themselves with keeping the peace amongst the various species that remained in orbit. Tasha Lem officially changed the core tenets of the Papal Mainframe's constituent chapters so that they became dedicated to ensuring that silence would fall in response to the question, turning the Papal Mainframe into Church of the Silence.

By the time of the Doctor and Clara's next visit to the Mainframe, it had been largely overrun by the Daleks, who converted most of the crew, including Lem herself, into puppets. However, with the Doctor's assistance, Tasha managed to resist the Daleks' control and take back the Church, and spend the remainder of conflict coordinating the Papal Mainframe and the Silence against the Daleks. (TV: The Time of the Doctor)

Colonel Manton lowered the hoods of the headless monks on the authority of the Papal Mainframe — an act that was otherwise a Level One Heresy. When Manton took the action at Demons Run, the Papal Mainframe was also commanded by a woman. (TV: A Good Man Goes to War)

Behind the scenes
Complexe Papal
 * In non-narrative sources, the Papal Mainframe was said to be the leader of the Headless Monks (REF: Doctor Who: The Encyclopedia) or the Church. (REF: The Brilliant Book 2012)
 * Following their return to their own time, Vastra and Jenny were added to the Papal Mainframe's "most wanted" list. (REF: The Brilliant Book 2012)
 * In TV: A Good Man Goes to War, Manton refers to "the Papal Mainframe herself", suggesting it is a title or office. TV: The Time of the Doctor reveals that the term properly refers to the church's spacefaring headquarters. Manton's phrasing would therefore be analogous a person referring to an order from the real-world Pope of the Catholic Church as coming from "Rome himself" or "the Vatican himself".