Take for example: [...] I'm saying such a scrambling happens all the time anyways, and that preserving the exact relative position, concentration, folding status etcetera may not be all that important to the cognitive system at large, at least we don't fret about it when shaking our heads. Does that help? Edit to respond to your edit: [...] I'd say it's an important point (naturally). If there were only one-to-one mappings, that would certainly be sufficient to establish that information-theoretically the original state information isn't lost. But that's a red herring, since we don't even need that strong a claim to argue for the theoretical viability of cryonics: When voluntarily shaking your head (you madman!) you were content with a much, much more forgiving standard. That's the one that should be used for such discussions.