The entire paper is one hypothesis. There are not more that I am aware of. — noAxioms

I wasn't sure whether to call the three numbered propositions you quoted hypotheses or axioms or what. I see that you call them possibilities, which is fine by me.

I posted his definition of 'posthuman', which is, in short, a level of technology capable of running the numbers he underestimates, and far worse, capable of simulating a posthuman set of machines doing similar simulations. — noAxioms

You did indeed. I didn't pay enough attention. Sorry. On the other hand, I'm not sure that it really matters very much whether we classify a civilisation with that technology as post-human or not.

There are no dinosaurs (which, unlike humans, is a collection of species). The vast majority of those species were simply ousted. They have no descendants. But some do, and the alligators and birds are their descendants. They are not dinosaurs because none of them is sexually compatible with any species that was around when the asteroid hit. They are post-dinosaur. — noAxioms

You are right. I think that's a better articulation than mine. I reckoned that picking a specific species would have the same problem as dinosaurs, since there can many sub-species of a given species, not to mention varieties of species and sub-species.

Prediction of what? A simulation of history makes no predictions. A simulation of the future is needed for that, hence the weather predictors. — noAxioms

Yes. This is muddled. Sorry. I was thinking of Bostrom's predictions.

To guess at the question, no simulation of any past Earth state will produce 'what actually happens', especially if that simulation is of evolutionary history. There is for instance no way to predict what children anybody will have, or when, so none of the famous people we know will appear in any simulation. Again, Bostrom seems entirely ignorant of such things, and of chaos theory in general. — noAxioms

Yes, that is what I was after. Thanks.

One can imagine the machine race actually getting curious about their origins, and knowing about humans and presumably having some DNA still around, they might run simulations in attempt to see how machines might emerge from that. — noAxioms

They might, and they might not. Imagination is a great thing. However, I can imagine several different scenarios. It seems to me quite likely that we will fail to control climate change and fail to adapt sufficiently, so either reverting to a pre-technological society or dying out. Or we might develop effective space flight and colonization and leave Earth. Or some idiot might starts an all-out war - atomic, biological and chemical. Or we realize the threat from the machines and destroy all the machines that might threaten us before they can take over. Or aliens might arrive and knock heads together until sanity is established. The possibilities are endless. I'm spoilt for choice. Like Buridan's ass, I need a reason to choose which to take seriously.

You seem to think I cannot refer to anything that I have not experienced. But the reference of a word is established in the language in general, not by what I may or may not have experienced. — Ludwig V

Then you also do not understand what causal link is -- and this is what the BIV theory is pointing out.

So when I can refer to the President of the United States even if I don't know that Joe Biden is the President. — Ludwig V

Right sentiment, wrong example.

Then you also do not understand what causal link is -- and this is what the BIV theory is pointing out. — L'éléphant

I wouldn't claim to understand what a causal link is. Tracking back our exchanges here, I realize that we have both been indulging a favourite trope in philosophy - accusing the other of not understanding what something is because the other has a different philosophical idea of what it is. It isn't at all constructive.
My current favourite examples is Searle:-

I think we all really have conscious states. To remind everyone of this fact I asked my readers to perform the small experiment of pinching the left forearm with the right hand to produce a small pain.

New York Review - Searle vs Dennett
Which begs to the question.

But we're also trying to respect the topic of the thread, so we're a bit trapped.

On the BiV, I had the impression that the Putnam's intention was to point out that Descartes' nightmare is an empirical possibility and that the causal theory of reference was presupposed. But I wouldn't want to be dogmatic about that.
The basis of my scepticism about what the BiV establishes is the private language argument (Stanford Encyclopedia)

I agree that reference is established by some sort of baptism ceremony (ostensive definition), though what that might consist of in practice is very flexible. We can think of two ceremonies. One establishes the public use of the term (think of the public naming of a ship); the other establishes the use for a specific speaker. In either case, there needs to be some sort of historical story that connects the ceremony with each occasion of use. Whether that amounts to a causal link depends heavily on one's definition of causality.
In addition, what one says about the BiV depends on whether what is referred to by a given term depends on the intention of the speaker or on the publicly established use of the term. Both theories are viable, in the sense that there are some philosophers who accept each of them. I think each has its place.

Right sentiment, wrong example. — L'éléphant

I wasn't happy with the example when I wrote it down. I was writing in haste and couldn't think of anything better.
But there is a problem. I am reminded of the paradox in the Meno about how one can recognize new knowledge when one is looking for it. Here, the paradox is that I must know something about the item I am referring to if I am to refer to it. So in one sense, I must know what a mule is when I refer to it. At the same time, it seems just obvious that I can refer to my mule (who is called "Freddy") without knowing that it is, by definition, an animal whose mother is a horse and whose father is a donkey. Perhaps you can think of a better example? (Though there may be more than one way.)