Is information-theoretic death the most real interpretation of death?

Of course. You are not dead until it becomes completely impossible to revive you, independent of currently available technology.

If we want the concept of death to be useful at all, it seems obvious that the only, and only the, irrecoverable death is the correct death.

As there is nothing beyond the material world, the mind is nothing but physical matter. If the physical matter is reconstructed, then the mind will have returned.

Atoms are fungible. If you swap one atom in your head for another atom, you've actually changed nothing. Ditto when you swap every atom in your head. Reconstructing your brain atom-for-atom would reconstruct you. But that's (ironically?) an overkill. Reconstructing neural structures will suffice.

Some people claim a reconstructed you is not really you, because there's a break in the continuity of consciousness. However, if continuity was important, you wouldn't want to fall asleep, let alone go under a general anesthetic, where your brain is so dead during the multi-hour surgery that when you wake up it feels like only five minutes has passed.

Cute video on identity.

If someone is unconscious but breathing, they're probably sleeping or passed out or in a coma. If someone is unconscious and not breathing, and does not have a pulse, we say they're dead. Isn't this dividing line obsolete? Given all we know about the mind by now, why are we still identifying life with respiration? Maybe it was the most important and interesting thing about our distant ancestors many millions of years ago, but not anymore. The essence of one's identity is not in the lungs or the heart. It is a pattern of information in the brain, and as long as that pattern is preserved, the description of "alive" is no more inappropriate than it is for a sleeping or comatose person.

I hereby decree that the state currently known as "death" shall henceforth be known as "necrogenesis" until information-theoretic death has occurred. The latter state shall be referred to simply as "death".

Right now, allowing necrogenesis to progress to death holds an arbitrary privileged status as the normal, morally acceptable thing to do. That's not how it should be. Seeing someone in necrogenesis and not making any attempt to preserve the essence of their identity before they die should be viewed as comparable to euthanasia at best, negligent homicide at worst.

The legal definition of death isn't based on anything more fundamental than the limits of medical science at the time the law was written, and in fact in many countries people would qualify as legally dead are rescusitated on a routine basis. So it seems perfectly reasonable to say that real death is the point beyond which no possible medical advance could revive you.

If the information defining a person is still around, that person can in principle be rebuilt.