Being a process doesn't preclude something from being an entity. In particular, all of us living organisms have our constituent atoms constantly replaced, and we don't typically consider that a risk to our sense of self.
It comes down to "what stays the same when all its atoms are replaced" and "how can we tell it is the same entity and not just an identical but different one". I think the answers are "shape" AND "continuity".
E.g. all "atoms" of a glider in Conway's Life get replaced every couple turns but an observer can tell it is still a glider because it keeps the shape, and it the same glider because it continues it's previous state.
This makes AI not quite alive because it's missing the continuity.
Sorry, it was more of a "shower thought" than a serious statement. The borders are blurry. Maybe it is alive. Maybe everything is alive. Maybe it is all relative. Humans classify as separate entities only on certain zoom level - zoom in and you get a symbiotic colony, zoom out and all you see is a population. Maybe AI is alive but only in the short time during inference. Maybe a continuously running claw is closer to a multiple generations of an organism going through evolution on each inference step. I am just musing.
My experience and intuition beg to differ. As I see it, much of our civilization progress is based on this redefinition of processes as entities, with some examples being: a sports team, a mathematical function, a loan, a company, a computer program and even the idea of a civilization itself.
