A question about a book...

[Romulator]

I'm sure you can base it off the events of SOMA, but I would recommend against referencing things by their direct names. The ARK is an acronym of the term Augmented Reality Capsule (with the C being changed to a K), which simply is another imaginative construction of putting humans into unusual environments which has been done in many science fiction media for long since before I was born.

You can take the idea of a floating computer-like object which has preserved humanity or basically anything else (environments, science, etc), have it crash into the sun, but make no reference whatsoever to the ARK or Pathos-II or other terms used in there to avoid potential plagiarism.

Furthermore, while I don't see too many issues with setting the story in the same universe as SOMA, you do have to deal with some continuity problems. For example, supposedly Sarah Lindwall in Tau is the last living person on Earth, and there aren't too many living conditions available on the surface according to a range of logs, distress calls and conversations.

If you're coming up with a narrative, but want to avoid plaigiarism and copyright, then use rely on subtle references and don't use names. Shape the events of SOMA, or some of the ideas in SOMA, to suit your narrative better.