No, when you carry through the calculations you will find that in equilibrium the density is monotonic with distance from the asteroid.

One easy way to see this: if there were increased density near the shell without any counterbalancing force attracting them to the shell, then there would be a net flow of particles away from the shell reducing the density. So this cannot be an equilibrium.

There may be transient microscopic density variations, but no macroscopic ones (absent some sort of Maxwell's Demon).

It is also an incorrect assumption that the motion is nearly radial. At all heights the direction distribution is still uniformly random.

There are O(n) sorting methods for max-sorting bounded data like this, with generalized extensions of radix sort. It's bounded because C_i is bounded below by the minimum cost of evaluating C_i (e.g. 1 FLOP), and P_i is bounded above by 1.

Though yes, bounded rationality is a broad class of concepts to which this problem belongs and there are very few known results that apply across the whole class.

You don't need O(n log(n)) sorting, but the real problem is that this is a problem in bounded rationality where the cost of rational reasoning itself is considered to come from a limited resource that needs to be allocated.

Literally steal?  No, except in cases that you probably don't mean such as where it's part of a building and someone physically removes that part of the building. "Steal" in the colloquial but not in the legal sense, sure.

Legally it's usually more like tortious interference, e.g. you have a contract that provides the service of using that space to park your car, and someone interferes with that by parking their own car there and deprives you of its use in an economically damaging way (such as having to pay for parking elsewhere). 

Sometimes it's trespass, such as when you actually own the land and can legally forbid others from entering.

It is also relatively common for it to be both: tortious interference with the contracted user of the parking space, and trespass against the lot owner who sets conditions for entry that are being violated.

Markets usually take some time to resolve, and money has a time value. Paying only $10 seems incredibly cheap for tying up a million dollars for even one day, and cheaper still when you consider any of the possible risks of putting $1M into a market that claims to resolve N/A with 99.9% chance.

Granting for the sake of argument that a superintelligence can determine that the universe in which it exists has an associated objectively "true" moral system in some sense, what requires it to conform to that system?

In short "I believe that there exists an objectively privileged system in which X is wrong" is far from equivalent to "I believe that X is wrong". Even the latter is far from equivalent to "I will not do X".

There are multiple additional weaknesses in the argument, some of which are addressed by other commenters.

I'm somewhat confused by the example at the end. SHA-3 (and other hash functions) are not injective, so it's not at all clear what "the preimage" means here. The example appears to choose a preimage of length 512 bits (matching the output), but SHA-3 is not designed to be injective on that domain either. It almost certainly is not, and therefore also not surjective so that some bitstrings have no such preimage.

It would be possible to restrict the chosen preimages further, e.g. to the lexicographically first preimage, but then just knowing that SHA3(x) = y does not guarantee that x is the preimage as defined.

Maybe a function that is guaranteed to be bijective yet difficult to invert would work better here?

Absolutely agreed. Wider public social norms are heavily against even mentioning any sort of major disruption due to AI in the near future (unless limited to specific jobs or copyright), and most people don't even understand how to think about conditional predictions. Combining the two is just the sort of thing strange people like us do.

Yes, it would be difficult to hold belief (3) and also believe that p-zombies are possible. By (3) all truthful human statements about self-OC are causally downstream from self-OC and so the premises that go into the concept of p-zombie humans are invalid.

It's still possible to imagine beings that appear and behave exactly like humans even under microscopic examination but aren't actually human and don't quite function the same way internally in some way we can't yet discern. This wouldn't violate (3), but would be a different concept from p-zombies which do function identically at every level of detail.

I expect that (3) is true, but don't think it's logically necessary that it be true. I think it's more likely a contingent truth of humans. I can only have experience of one human consciousness, but it would be weird if some were conscious and some weren't without any objectively distinguishable differences that would explain the distinction.

Edit: On reflection, I don't think (3) is true. It seems a reasonable possibility that causality is the wrong way to describe the relationship between OC and reports on OC, possibly in a way similar to saying that a calculator displaying "4" after entering "2+2" is causally downstream of mathematical axioms. They're perhaps different types of things and causality is an inapplicable concept between them.

I disagree with (4) in that many sentences concerning nonexistent referents will be vacuously true rather than false. For those that are false, their manner of being false will be different from any of your example sentences.

I also think that for all behavioural purposes, statements involving OC can be transformed into statements not involving OC with the same externally verifiable content. That means that I also disagree with (8) and therefore (9): Zombies can honestly promise things about their 'intentions' as cashed out in future behaviour, and can coordinate.

For (14), some people can in fact see ultraviolet light to an extent. However it apparently doesn't look a great deal different from violet, presumably because the same visual pathways are used with similar activations in these cases.