The Papal Mainframe was the headquarters of the Church: the militarised, syncretic religious order headed by the Mother Superious Tasha Lem, which later reformed into the Silence during the Siege of Trenzalore.
Due to its being the Mother Superious's headquarters, the Church was sometimes referred to as "the Church of the Papal Mainframe", even after it became the Church of the Silence (TV: The Time of the Doctor), and Colonel Runaway once spoke by metonymy of "the Papal Mainfraime herself" to refer to the Mother Superious (TV: A Good Man Goes to War).
Behind the scenes
- In A Good Man Goes to War, Manton refers to "the Papal Mainframe herself", suggesting it is a title or office. The Time of the Doctor reveals that the term properly refers to the Church's spacefaring headquarters, while the title of the religious leader is actually Mother Superious. 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"; the correct phrasing would be "the Mother Superious of the Papal Mainframe herself." However, Manton's remark remains problematic in another respect: Time of the Doctor revealed that the branch of the Silence led by Kovarian, which was the one featured in A Good Man Goes to War, had seceded from the authority of Tasha Lem and the Mainframe. It is thus unclear why its permission would be relevant to Manton's actions.