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 read the text.

He was summoned to the Vatican to investigate the Veritas. The Doctor, Bill and Nardole entered 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. They 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.

There, Nardole discovered the truth. Stepping beyond the field of the projectors he ceased to exist. Bill re-encountered the Doctor on the Oval Office, where the President had taken an overdose. The Doctor explained that they were simulations and they were confronted by their creators. The Monks deleted Bill from the system and the Doctor, facing deletion himself, emailed the events to his real self. (TV: Extremis)