Everything known about these events comes from narrative compilations assembled a century and a half or more later, under dynasties with a stake in how the story came out, drawing on reports transmitted through partisans of one side or another. The compilers themselves were often scrupulous, setting variant accounts side by side with their chains of transmission, which is a service to later historians and also an admission that they could not always tell which was right.
Modern scholarship divides on what to do about this. Some historians reconstruct a coherent narrative from the reports, weighing the transmitters much as the tradition itself did. Others hold that the material has been shaped too thoroughly by later doctrinal concerns to support that kind of reconstruction, and argue that the accounts tell us more about the third century of Islam than about the first. Wilferd Madelung's study of the succession is a sustained argument for taking the early material more seriously than the sceptical position allows.
The atlas records the war, its phases and its outcome, because these are attested across sources with different sympathies and the general course is not seriously in doubt. It does not adjudicate the questions the sources were written to settle: who was right about Uthman, whether Ali should have arbitrated, and whether the community's choice was legitimate. Those are the questions that made the divisions, and no historian settles them from outside.