My response to this is very simple, but it's necessary to know beforehand that the brain's operation is robust to many low-level variations, e.g., thermal noise that triggers occasional random action potentials at a low rate.
We would have to have a great many trial runs and would decide when we had got it right.
Suppose our standard is that we get it right when the reconstructed brain is more like the original brain just before cryonic preservation than a brain after a good night's sleep is like that same brain before sleeping -- within the subset of brain features that are not robust to variation. Further suppose that that standard is achieved through a process that involves a representation of the structure of the brain. Albeit that the representation is indeed a "cultural practice", the brute fact of the extreme degree of similarity of the pre- and post-process brains would seem much more relevant to the question of preservation of any aspect of the brain worthy of being called "identity".
ETA: Thinking about this a bit more, I see that the notion of "similarity" in the above argument is also vulnerable to the charge of being a mere cultural practice. So let me clarify that the kind of similarity I have in mind basically maps to reproducibility of the input-output relation of a low-level functional unit, up to, say, the magnitude of thermal noise. Reproducibility in this sense has empirical content; it is not merely culturally constructed.
I don't see how using more detailed measurements makes it any less a cultural practice. There isn't a limit you can pass where doing something according to a standard suddenly becomes a physical relationship. Regardless, consider that you could create as many copies to that standard as you wished, so you now have a one-to-many relationship of "identity" according to your scenario. Such a type-token relationship is typical of norm-based standards (such as mediums of representation) because they are norm-based standards (that is, because you can make as many according to the standard as you wish).
In June 2012, Robin Hanson wrote a post promoting plastination as a superior to cryopreservation as an approach to preserving people for later uploading. His post included a paragraph which said:
This left me with the impression that the chances of the average cryopreserved person today of being later revived aren't great, even when you conditionalize on no existential catastrophe. More recently, I did a systematic read-through of the sequences for the first time (about a month 1/2 ago), and Eliezer's post You Only Live Twice convinced me to finally sign up for cryonics for three reasons:
I don't find that terribly encouraging. So now I'm back to being pessimistic about current cryopreservation techniques (though I'm still signing up for cryonics because the cost is low enough even given my current estimate of my chances). But I'd very much be curious to know if anyone knows what, say, Nick Bostrom or Anders Sandberg think about the issue. Anyone?
Edit: I'm aware of estimates given by LessWrong folks in the census of the chances of revival, but I don't know how much of that is people taking things like existential risk into account. There are lots of different ways you could arrive at a ~10% chance of revival overall:
is one way. But:
is a very similar conclusion from very different premises. Gwern has more on this sort of reasoning in Plastination versus cryonics, but I don't know who most of the people he links to are so I'm not sure whether to trust them. He does link to a breakdown of probabilities by Robin, but I don't fully understand the way Robin is breaking the issue down.