Paradox TARDIS

The Paradox TARDIS was a TARDIS built by Sibling Same and Sibling Different in order to stabilise themselves in reality after the end of the Last Great Time War threatened to erase them completely. The TARDIS was constructed from parts of alternate timeline versions of the Doctor's TARDIS. (PROSE: The Paradox Moon)

History
When the Doctor ended the Last Great Time War, Siblings Same and Different were partially erased from existence and reduced to ghost-like creatures. To fully stabilise themselves in reality once again, the Siblings used the paradox energy that comprised themselves to break into alternate timelines, including dead timelines, and attempted to steal these timelines' versions of the Doctor's TARDIS. However, when Sibling Same reasoned that the Doctor would always pursue them if they stole the Doctor's TARDIS, he suggested an alternative plan; to build the Paradox TARDIS, a TARDIS comprised of components from alternative timeline versions of the Doctor's TARDIS.

Siblings Same and Different explored many alternate timelines to scavenge the Doctor's TARDIS, and eventually finished constructing the Paradox TARDIS in N-Space, eventually materialising above the Shadow Proclamation as a moon. Six hours later, the Thirteenth Doctor travelled to the Shadow Proclamation in response to the Paradox TARDIS' distress call, and, after being informed of the "moon" by the Shadow Architect, teleported to the TARDIS with Sibling Different - masquerading as "Mae" - and Praetorian X-B1, arriving in a house resembling one from 20th century Earth. The Doctor, Mae and X-B1 explored the house, and eventually found the Paradox TARDIS' control room; when Sibling Different abandoned her disguise and shot X-B1, Sibling Same revealed himself, and the two Siblings activated the Paradox TARDIS. However, after being persuaded by the Doctor, Sibling Same allowed the various components of the Paradox TARDIS to dematerialise back to their respective timelines, before transferring the last of his paradox energy to Sibling Different, thereby stabilising her in reality at the cost of Same's life. As a result, the Paradox TARDIS ceased to exist. (PROSE: The Paradox Moon)