Shadow World

The Shadow World was a virtual simulation of Earth, inhabited by virtual constructs of the planet's populace, made by the Monks in order to prepare for a real invasion.

When the individuals within the world discovered they were merely simulacra, they committed suicide and deleted themselves from the "game". (TV: Extremis) There appeared to be numerous Shadow worlds that the Monks had created. (TV: The Pyramid at the End of the World)

History
The history of the Shadow World, at least up until 2017, was much the same as that of Earth. However, in this world existed an ancient text in a secret library beneath the Vatican - the Veritas.

In 2017, the Veritas was translated and all but one of the translators were discovered dead by their own hand. The Pope met with the Twelfth Doctor at St Luke's University and asked him to come to the Vatican to read the text.

The Doctor took Bill and Nardole with him to the Haereticum, where they discovered that the missing translator had emailed the text to various contacts, including CERN. Bill and Nardole found a portal to a room full of projectors, which led to other locations, including the Pentagon, CERN and the White House. Travelling to CERN, the pair were invited to attend a mass suicide and were asked to pick a series of random numbers, only to find that the sequence was pseudorandom. They returned through the portal just as CERN was detonated.

In the projector room, Nardole discovered the truth, and to prove his suspicions, stepped beyond the field of the projectors, causing him to turn into pixels. Bill stepped through another portal and re-encountered the Doctor at the Oval Office, where the President had taken an overdose. The Doctor explained that they were simulations before they were confronted by the Monks, who deleted Bill from the system. Before he too was deleted, the Doctor used his sonic sunglasses to email a recording of the events to his real self. (TV: Extremis)