> What they are claiming that they are preserving some record of the information that makes you up on the hope that it would be sufficient for future engineers to reconstruct some version of you.
Yes, that's what they are claiming, but there is zero proof this is going to happen. In fact, given the long term stability of real world artifacts that are far more durable than dewar flasks there are substantial obstacles in the way of success here besides the non-viable scientific parts of it.
The whole point is that this is a 'hope' about as useful as the hope that there is a heaven or a life after death.
Death is final, until proven otherwise, and once if it is proven that it isn't we will know the pre-conditions required for successful preservation.
Keep in mind that freezing the brain actually destroys it further, the resulting structures may look like they still preserve information when in fact they probably won't, just like a frozen and then thawed out steak still looks like the original but has structurally been completely altered.
> All they are claiming is that cryonic vitrification or aldehyde-stabilized cryopreservation preserves in an information-theory sense the microstructure of the brain to sufficient detail that the connectome can be reconstructed by physically realizable scanning mechanisms, which we might not have now but are permitted by the laws of physics.
The laws of physics have little to do with it, it all depends on how much - if anything - of value is still present and recoverable from dead tissue. So far there is no proof that high level constructs such as memories and identity would be preserved through such a cycle.
> That's a much weaker argument, but one which actually IS supported by actual scientific papers in the field.
Actual scientific papers are not the equivalent of proof, they are merely the advancement of theories in the scientific sense, lacking - for now - evidence supporting those theories.
Cryonics organizations are very careful to ride that fine line between selling hope and selling bull-shit. They have to because that's where the gullible nerds will be more than happy to part with their money.
The short version of all this is:
Hope Springs Eternal.
And hope for an eternal life is common to Catholics looking for salvation, uploaders, cryogenic preservers and rapture kooks. And they all have another thing in common too: they all die anyway, just like everybody and everything else that is alive.