I as a physical agent may very well be short-lived myself. Identity is simply a preferences code that is implemented by every one of a set of possible physical agents, one of which is my body. An executable identity is maintained as the code of the physical system as long as it can as that. This seems to me only a matter of engineering or biology (based on physics) and the minimal influx of free energy to store the code without errors, as well as resource expenditure for my actions that you need to see if you want to register / keep registering me. (That is, if you disregard the astronomically unlikely quantum events.) The preceding applies to any kind of identity, human or otherwise.

> get an "immutable-looking" entity out of mutable substance

That substance, though having a changing state, is governed by immutable (as we notice so far) laws of physics (more directly, emergence of life, evolution, human biology and any natural laws that technology depends on). That's how I feel that this immutability is valid.

If you want, you can regard my identity as a little "physical/natural law" generated around my body. So the law will be there as long as the body works. And, I think, in principle any body housing any identity can be maintained indefinitely given minimal free energy and mass influx (this requires technologies not yet available today) if you again set a target probability of random quantum changes. This applies to "distributed" identities equally.

> the reverse is not possible - getting mutable stuff out of immutable stuff

If one depends on arbitrary data from environment and there is not enough experimentation done by either one or the producers of the data, one becomes mutable. Mutate or be mutated.

> I as a physical agent may very well be short-lived myself...

You are explaining potential implementation methods, but I think implementation method is a secondary consideration. The more interesting question is what is the simpler and more likely explanation. I think envisoning thought as a sprawling system (through space/time), creating temporary localized identities, through clustering & evolving preferences is simpler than the one with non-mutating preferences. It is non-dualistic, doesn't require multiple layers, etc.

> That substance, though having a changing state, is governed by immutable (as we notice so far) laws of physics

You are mixing layers - substance & laws it seems to be governed by (law is a "meta" substance if you will, or properties derived from a given set of observations). To create immutability out of mutability, you need to build sophisticated layers... That makes it a more complex explanation (and less likely explanation).

Moreover, having a mutable/evolving identity doesn't preclude it from being governed by immutable laws.

Just a matter of applying occam's razor.