What it is for me to persist is for there to be, instantiated in some system, an algorithm with a particular relation to the algorithm which characterizes me at present. And I don't think algorithms are physical entities (though, in this universe they seem to be instantiated that way). I suppose you could define "physical" to mean any possible physics but even then the fact that an algorithm is instantiated physically doesn't mean it is identical to that physical entity (the instantiation). Plus any accurate physical description couldn't apply to the entirety of possible instantiations.
I gave up trying to talk my self out of Platonism a while ago.
What it is for me to persist is for there to be, instantiated in some system, an algorithm with a particular relation to the algorithm which characterizes me at present.
Emphasis added. I think "instantiates an algorithm of type X" qualifies as a physical specification in the relevant sense; Platonism is not a problem. However to answer the post you would need to define (or point us in the direction of) the "particular relation" you have in mind.
-