Does Altered Carbon show any ambiguity about the idea of personalities being stored and downloaded into new bodies being the same person? Or it's completely assured they are the same person? I mean, I dont know if it's a good comparison, but if I take the hard drive from a computer and put it into another, even when I'll have the same softwares and files (which might run or not by the way), it isnt the same computer. Does Altered Carbon play with this idea or it's assured through the whole story than the personalities being stored and downloaded into new bodies are the same persons? If I recall correctly, other sci fi stories which used a similar idea (passing one person's memories from one body into another) like "The 6th day", created new persons, not the same one.
In my mind that's a paradox, because "double-sleeving" is a deal breaker for the same-person argument. If you can double-sleeve that means the process is just copying. On the other hand, people are needle-casting to different sleeves and saving themselves to remote backups and dying all the time as if the newly spun up copy is still "them".
You could say the show just ignores the dilemma.
This is one of many ignored concepts in the show. I lost count of plot-holes, unscientific or plain illogical things in it.
I think the show deliberately ignores the issue. However, I think of it like this: As long as the stack is being moved from body to body I accept the premise that it is the same person. To use your computer analogy, I think of a "person" not as files, etc. (i.e. their memories) but as a "process" that runs on the stack. When a body dies the process simply hibernates and resumes when inserted into a new body.
The trouble begins with remote backups. Here I would no longer consider them the same person since it is a new "process" simply created from the same (or usually, slightly older) "files". On a computer this process would get a new
pid (process id) and would thus be a completely new but similar process.