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Psychohistorian comments on Is cryonics necessary?: Writing yourself into the future - Less Wrong
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Your question is a more complicated version of "what happens if I'm non-destructively copied", and the answer to that one is that both of them are you, and so before the copying is done you should assign equal probability to "ending up as" the original or as the copy. (It should work the same as Everett branching.)
In this case, I don't fully expect the "reconstructed from writings" self to be as connected to my current subjective experience as a cryopreserved self would be. But the mere fact of there being "two selves" doesn't present an inherent problem.
If I understand the physics and the link even a little bit correctly, those copies would have to be identical to an arbitrarily high degree of specification. That identicalness would end soon (I'd imagine something like nanoseconds) after the new brain was generated (and I think it's extremely charitable to posit that such a replication is meaningfully possible); it seems like even variations in local gravity would break the identity. Certainly, within a few seconds, processing necessarily different sensory data (as both copies can't be observing from the exact same location) would make the two different. What happens to double-me at that point, or is that somehow not material?
Well, ISTM that only the gross structure (the cells, the strength of their connections, and the state of firing) is really essential to the relevant pattern. Advanced nanotechnology is theoretically more than capable of recording such data and constructing a copy, to within the accuracy of body-temperature thermal noise. (So if you really wanted to be careful, you'd put the brain in suspended animation at low temperature, copy it there, and warm both copies back up to normal; but I don't think that would be necessary in practice.)
Yup, the copies diverge. Just as there are different quantum versions of me branching as life goes along (see here for a relevant parable), my experience would branch there, with two people who once were "me". When I observe a quantum random coinflip, half of future mes are in worlds where they observe heads and half are in worlds where they observe tails; they quickly become different people from each other, both of them remembering having been me-before-the-flip, and so it's quite coherent for me to say before the flip that I expect to see heads with 1/2 probability and tails with 1/2 probability. The duplication experiment is no different, except that this time my branched copies have the chance to play chess against each other afterwards. I expect 1/2 probability of finding myself to be the one who remained in the scanning room (and who gets to play White), and 1/2 chance of finding myself to be the one who wakes in the construction room (and who gets to play Black).