Nope. No.

PhD programs in mathematics, statistics, philosophy, and theoretical computer science tend to give you a great deal of free time and flexibility, provided you can pass the various qualifying exams without too much studying.

Bolding the parts to which I object.

I have never seen anyone in a rigorous postgraduate program who had a lot of free time and could pass their quals without large amounts of studying.

Of course, I could just be, like magic, on the lower part of the intelligence curve for graduate school, but given that my actual measured IQ numbers are pretty in-the-middle for scientific academia (I won't tell what they are, though), and given that almost everyone else says they have little free time and have to study hard in graduate school, I'm inclined to believe the bolded phrases only accurately describe a narrow slice of lucky individuals.

If a gap is about very important feature or a secret event, it could be two completely different people. Like if we don't know if a person of interest was a gay.

If we don't know 100 bits of information, we need to create 2 power 100 copies to fill all gaps. Even for FAI it may be difficult. Also it may be unpleasant to the copies themselves, as it would delude their value to outside world.

It could be solved by acasual trading between parallel worlds. I tried to explain it in the map under the title that DI stalks well with many world immortality.

If we have infinitely many worlds with the same evidence about the person ( but the person is different in different world, only the evidence is the same), we could create only one resurrection in each world which is in agreement with this evidence, AND it will be exact resurrection of the person from another world.

BUT, the person from this world will be exact resurrected in the another world, so each person will have exact resurrection in some world, and each world will have only one person which much its evidence. (So, no problems with ethics and resources.)

I think that it may be difficult to explain this in several lines, but I hope you grasp the idea. If it is not clear I could try better explanation.

We could solve it if we move from binary idea of identity, which only can be 0 or 1, me or not me, to continuous idea of identity, which could have many gradation. In this case we should ask how similar the copy will be to the original or what is the probability that I find my self in the next moment to be that copy. The main problems with identity is that it is wrong notion. It assumes that set of all possible observer is divided on many subset of observers, which are identical inside that subsets. But the idea identity is only useful to answer questions like "what I will feel in next moment". Most such question could be answered without binary conception of identity. Any way I suggest ti stick for now to conservative approach to identity problem - see comment above.

In case of DI, we should collect as much information as possible.

Saying that it's important doesn't mean it's simple.

You're confusing the intuitive notion of "simple" with "low Kolmogorov complexity". For example, the Mandelbrot set is "complicated" in the intuitive sense, but has low Kolmogorov complexity since it can be constructed by a simple process.

What do you mean by "short referent?" Yes, it will likely be an often-used concept, so the internal symbol signifying the concept is likely to be short, but that says absolutely nothing about the complexity of the concept itself.

It does if you look at the rest of my argument.

If you want to say that "agentiness" is a K-simple concept, perhaps you should demonstrate that by explicating a precise computational definition for an agent detector,

Step 1: Stimulation the universe for a sufficiently long time.

Step 2: Ask the entity now filling up the universe "is this an agent?".

Thus reducing entropy globally must have low Kolmogorov complexity.

What do you mean by that statement? Kolmogorov complexity is a property of a concept. Well "reducing entropy" as a concept does have low Kolmogorov complexity.

Kolmogorov's, which is of course the actual reason for my initial "k"s.

the whole "a godless universe has low Kolmogorov complexity" argument that you're trying to make.

It might, perhaps, if I were actually trying to make that argument. But so far as I can see no one is claiming here that the universe has low komplexity. (All the atheistic argument needs is for the godless version of the universe to have lower komplexity than the godded one.)

all the universes that can support life are likely to wind up taken over by AGIs.

Even if so, you still have the locate-the-relevant-bit problem. (Even if you can just say "pick any universe", you have to find the relevant bit within that universe.) It's also not clear to me that locating universes suitable for life within something like the Tegmark multiverse is low-komplexity.

the AGI can. [...] it's likely to have a short referent to it.

An easy-to-use one, perhaps, but I see no guarantee that it'll be something easy to identify for others, which is what's relevant.

Consider humans; we're surely much simpler than a universe-spanning AGI (and also more likely to have a concept that nicely matches the human concept of "agent"; perhaps a universe-spanning AGI would instead have some elaborate range of "agent"-like concepts making fine distinctions we don't see or don't appreciate; but never mind that). Could you specify how to tell, using a human brain, whether something is an agent? (Recall that for komplexity-measuring purposes, if you do so by means of language or something then the komplexity of that language is part of the cost you pay. In fact, it's worse; you need to specify how to work out that language by looking at human brains. Similarly, if you want to say "look at the neurons located here", the thing you need to pay the komplexity-cost of is not just specifying "here" but specifying how to find "here" in a way that works for any possible human-like thing.)

For your first premise to be uncontroversial around here, I think you need to either take it as applying only to the form of the laws of physics and not to initial conditions, arbitrary constants, etc. (in which case you can't identify "this universe" and still have it be of low complexity)

Doesn't that undermine the premise of the whole "a godless universe has low Kolmogorov complexity" argument that you're trying to make?

adopt something like Tegmark's MUH that amounts to running every version of the universe (all boundary conditions, all values for the constants, etc.) in parallel (in which case what gets taken over by a superintelligent AI is no longer the whole thing but a possibly-tiny part, and specifying that part costs a lot of complexity).

Well, all the universes that support can life are likely wind up taken over by AGI's.

unless you are depending on it taking over the whole universe so that you can just point at the whole caboodle and say "that thing" -- but then presumably its agent-detection facilities are a tiny part of the whole (not necessarily a spatially localized part, of course), and singling those out so you can say "agents are things that that identifies as agents" again has a large complexity cost from locating them.

But, the AGI can. Agentiness is going to be a very important concept for it. Thus it's likely to have a short referent to it.