Does anyone have any compelling arguments on why an FAI would or would not recreate me if I die, decompose, and then the singularity occurs a long time after my death?

A possible reason why not besides physical impossibility: are you sure you want to be recreated?---I don't mean to invoke any tired cishumanist tropes about death being the natural order of things or any nonsense like that. But it seems plausible to me that a benevolent superintelligence would have no trouble contriving configurations of matter that at least some of us would prefer to personal survival; specifically, the AI could create people better than us by our own standards.

Presumably you don't want to live on exactly as you are now; you have a desire for self-improvement. But given the impossibility of ontologically fundamental mental entities, there's an identity between "self-improvement" and "being deleted and immediately replaced with someone else who happens to be very similar in these-and-such ways"; once you know what experiences are taking place at what points in spacetime, there's no further fact of the matter as to which ones of them are "you." In our own world, this is an unimportant philosophical nicety, but superintelligence has the potential to open up previously inaccessible edge cases, such as extremely desirable outcomes that don't preserve enough personal identity to count as "survival" in the conventional sense.

This scenario is much farther along the impossible scale than reviving an intact brain. If I wanted to live forever, I would make absolutely sure that I had a plan that did not involve violating the laws of physics.

(Not that I'm an expert physicist, but my understanding is that decomposition is an irreversible process.)

Upvoted from -1 to 0 because the question is interesting and important; the fact that the answer seems clear to some is not cause for downvoting, in my view. (This is the Discussion section; would you have downvoted this post if it had been an Open Thread comment?)

As it happens, I don't think the answer is necessarily a settled matter, any more than time travel in general (of which this can be considered a special case) is. It seems quite possible that the universe may contain much more information about its past than we can currently envision being able to extract. (One might for instance compare the old belief that determining the chemical composition of stars was hopeless due to their distance.) Yes, thermodynamics may imply that not all of the past can be reconstructed, but it may not be necessary to extract all of it in order to reconstruct a few human minds. Presumably a huge (by present standards) expenditure of negentropy would be involved, but as far as I know the universe seems to contain a whole lot of "wasted" negentropy at the moment.

Depends what you mean by "recreating"; if you mean a copy that could fool anyone who knew all the relevant facts about that person into believing that it was, indeed, that person that they were dealing with, it's kind of obvious that a powerful AI could do it.

The question seems ill-posed. I know what "information-theoretically dead" means, I think I know what "dead by modern standards" means, but I'm not sure it's possible to make sensible the notion of "information-theoretically-dead by modern standards".

If long-range weather prediction is impossible in general, even assuming determinism and no random elements, then what you're describing, which would entail solving multiple chaotic dynamical systems, is "doubleplus impossible" in practice.

OK, let's make a few assumptions. Assume, for a start, that all the information in your brain is necessary to resurrect you, down to the quantum level. And that this is incompressible - that even computronium requires as much mass/energy as is contained in your brain in order to perfectly simulate it. But assume also that an FAI can convert matter/energy into computronium.

By the Bekenstein Bound, the absolute maximum number of brain states that could be possible is 10^(7.79640 10^41) , which we can approximate as 10^10^41. Note this is a SERIOUSLY HIGH estimate. That would be the number of possible states of any* roughly-spherical lump of matter of the right radius and mass. The mass of a brain is between one and two kilograms, so very roughly, we'd need 10^10^41 kg of computronium to simulate every possible brain state.

The mass of the galaxy is 10^42 kg, so the mass of the galaxy is exponentially smaller than the mass that would be needed to simulate every possible brain state.

So that's an upper limit - but that limit rests on wanting simulations of every possible brain state to exist simultaneously, where 'brain state' means everything from the state my brain is in now, to the state it was in one nanosecond ago, to the state that a 1.5kg bag of sugar was in half an hour ago, to...

If we wish to limit ourselves to brains that have existed, then the figure could be much lower. By definition, every human brain thus far has been made from the mass on the earth's crust and atmosphere, and there have been roughly a hundred billion people ever - they could easily be computed if we had precise data about their states, using considerably less mass than that of the Earth.

So the question becomes, is there any way of winnowing down the 'possible brain states' to the 'have-existed brain states'? I would expect so, to quite a large extent. Firstly, you'd only want to use those brain states that correspond to actual states of human brains - the state that corresponds to being a chunk of my armchair could be thrown away. That in itself would get rid of the vast bulk of possible states of matter.

Secondly, most of the resulting states would be duplicates. There would be my brain now, my brain a second ago, my brain as it would be in a universe where I'd chosen a different pair of socks this morning but otherwise nothing was different... I don't think anyone in the world would have any actual problem (as opposed to philosophical problems) identifying those people as one individual.

Thirdly, we can limit by known history. Obviously as one goes further back, what 'known history' is is foggier, but we can, for example, not simulate any brains whose memories would require them to have been born on Alpha Centauri in the year 5BC and to be 12 in the year 2032 - getting rid of brains with logically inconsistent or physically impossible pasts would winnow it down some more.

And finally, if all else fails, you can brute force the problem over multiple universes. Of the brains that are left to be simulated, select a subset of them to simulate using a quantum experiment, and leave the others to other aspects of the multiverse (this is assuming the multiversal interpretation of quantum physics to be correct, but I would imagine that a greater-than-human intelligence would have some way of confirming this beyond all doubt).

So my own thought is it's physically possible (assuming a situation where a FAI exists, which is a whole other problem in itself), but extraordinarily difficult. I would not expect it to happen unless and until a good proportion of the galaxy was converted to computronium. But should that happen, and should a FAI exist, then it would pretty much be the definition of 'friendliness' that it would resurrect people, starting with those easiest to bring back.

My own guesstimate is that, conditional on FAI being achieved in the next 100 years (so enough information is preserved to make them relatively easy to resurrect), and conditional on it being able to use mass utterly efficiently for computation, then there is probably as great as a 40% chance that those alive today but dead before FAI is created would eventually be resurrected with enough fidelity that they couldn't themselves tell the difference. How high you put the probability of FAI and computronium is, of course, up to you.

One approach that might work rather than simulating physics backwards (which strikes me as implausible given the nature of quantum mechanical effects) would be to analyze the information coming back from interstellar dust particles. This would tend to be impacted only by sources of light and gravity at a given precise distance.

Thus a crude model of the large planetary bodies of the solar system at a given moment could be calculated by triangulating information from the correct set of dust particles, which could be refined over time, as new data points are added, to indicate large land masses, and eventually resolved into human bodies and their individual atoms. This should be sufficient to resurrect everyone from their moment of death, as well as restoring every memory they ever forgot.

I don't see this as a good substitute for cryonics because there are plausible universes where FAI is e.g. self limiting in a way that would prevent it from converting the solar system (perhaps the galaxy) into computronium, which I think would probably be a minimal prerequisite to actually pulling something like this off. I also think an intelligence explosion scenario is not inevitable (may be impossible or extraordinarily unlikely for some reason), and that cryonics can work with incremental human-level improvements in technology.

Even in the high-speed fooming FAI class of scenario, such tasks as converting the galaxy to computronium, and collecting enough data from enough points, are limited by the speed of light factor and might take hundreds of thousands of years, if not millions. In the mean time, those who are cryopreserved could be up and walking around, forming new experiences and laying the groundwork for future civilization. They would also be more likely to have opportunities to take part in early interstellar and intergalactic colonization efforts.

It might be possible if there are a lot of information available about you, e.g. chat transcripts, videos and people who knew you very well. This is called a beta level simulations as described in some of Alastair Reynolds’ novels.

Resurrection without a backup. As with ecosystem reconstruction, such "resurrections" are in fact clever simulations. If the available information is sufficiently detailed, the individual and even close friends and associations are unable to tell the difference. However, transapient informants say that any being of the same toposophic level as the "resurrector" can see marks that the new being is not at all like the old one. "Resurrections" of historical figures, or of persons who lived at the fringes of Terragen civilization and were not well recorded, are of very uneven quality.

Encyclopedia Galactica - Limits of Transapient Power

The above is of course fictional evidence but I think the idea is very interesting and might not be impossible given a large amount of information and a superhuman AI.

It might work even better if some of your DNA is available so that you can be cloned and your clone imprinted with recordings, extrapolations and behavioural patterns based on lifelogs. I suppose that even without a DNA sample, given sufficiently powerful AI, such a beta-level simulation might be sufficiently close so that only a powerful posthuman being could notice any difference compared to the original. At least that's a nice idea :-)

ETA In any case, I'd go with cryonics. Because beta-level simulations are just crude simulations. Further I believe that if you don't want to go with cryonics you can find some reassurance in the many many-worlds ideas. MWI, the simulation argument, dust theory, Tegmark's mathematical universe etc. If one of them is factual, there will be some "copies" of you alive and happy somwhere.

I would advise using cryonics in any case, because you could be wrong and it makes the FAI's job easier.

EDIT: What about time travel?