1. By "optimal", I mean in an evidential, rather than causal, sense. That is, the optimal value is that which signals greatest fitness to a mate, rather than the value that is most practically useful otherwise. I took Fisherian runaway to mean that there would be overcorrection, with selection for even more extreme traits than what signals greatest fitness, because of sexual selection by the next generation. So, in my model, the value of $X$ that causally leads to greatest chance of survival could be $-1$, but high values for $X$ are evidence for other traits that are causally associated with survivability, so $X=0$ offers best evidence of survivability to potential mates, and Fisherian runaway leads to selection for $X=1$. Perhaps I'm misinterpreting Fisherian runaway, and it's just saying that there will be selection for $X=0$ in this case, instead of over-correcting and selecting for $X=1$? But then what's all this talk about later-generation sexual selection, if this doesn't change the equilibrium?
2. Ah, so if we start out with an average $X=-10$, standard deviation $1$, and optimal $X=0$, then selecting for larger $X$ has the same effect as selecting for $X$ closer to $0$, and that could end up being what potential mates do, driving $X$ up over the generations, until it is common for individuals to have positive $X$, but potential mates have learned to select for higher $X$? Sure, I guess that could happen, but there would then be selection pressure on potential mates to stop selecting for higher $X$ at this point. This would also require a rapid environmental change that shifts the optimal value of $X$; if environmental changes affecting optimal phenotype aren't much faster than evolution, then optimal phenotypes shouldn't be so wildly off the distribution of actual phenotypes.

Fisherian runaway doesn't make any sense to me.

Suppose that each individual in a species of a given sex has some real-valued variable $X$, which is observable by the other sex. Suppose that, absent considerations about sexual selection by potential mates for the next generation, the evolutionarily optimal value for $X$ is 0. How could we end up with a positive feedback loop involving sexual selection for positive values of $X$, creating a new evolutionary equilibrium with an optimal value $X=1$ when taking into account sexual selection? First the other sex ends up with some smaller degree of selection for positive values of $X$ (say selecting most strongly for $X=.5$). If sexual selection by the next generation of potential mates were the only thing that mattered, then the optimal value of $X$ to select for is $.5$, since that's what everyone else is selecting for. That's stability, not positive feedback. But sexual selection by the next generation of potential mates isn't the only thing that matters; by stipulation, different values of $X$ have effects on evolutionary fitness other than through sexual selection, with values closer to $0$ being better. So, when choosing a mate, one must balance the considerations of sexual selection by the next generation (for which $X=.5$ is optimal) and other considerations (for which $X=0$ is optimal), leading to selection for mates with $0<X<.5$ being evolutionarily optimal. That's negative feedback. How do you get positive feedback?

I know this was tagged as humor, but taking it seriously anyway,

I'm skeptical that breeding octopuses for intelligence would yield much in the way of valuable insights for AI safety, since octopuses and humans have so much in common that AGI wouldn't. That said, it's hard to rule out that uplifting another species could reveal some valuable unknown unknowns about general intelligence, so I unironically think this is a good reason to try it.

Another, more likely to pay off, benefit to doing this would be as a testbed for genetically engineering humans for higher intelligence (which also might have benefits for AI safety under long-timelines assumptions). I also think it would just be really cool from a scientific perspective.

One example of a class of algorithms that can solve its own halting problem is the class of primitive recursive functions. There's a primitive recursive function $F$ that takes as input a description of a primitive recursive function $A$ and input $I$ and outputs $true$ if $A\left(I\right)$ halts, and $false$ otherwise: this program is given by $F(A,I)=true$, because all primitive recursive functions halt on all inputs. In this case, it is $R$ that does not exist.

I think $C$ should exist, at least for classical bits (which as others have pointed out, is all that is needed), for any reasonably versatile model of computation. This is not so for $R$, since primitive recursion is actually an incredibly powerful model of computation; any program that you should be able to get an output from before the heat death of the universe can be written with primitive recursion, and in some sense, primitive recursion is ridiculous overkill for that purpose.

If a group decides something unanimously, and has the power to do it, they can do it. That would take them outside the formal channels of the EU (or in another context of NATO) but I do not see any barrier to an agreement to stop importing Russian gas followed by everyone who agreed to it no longer importing Russian gas. Hungary would keep importing, but that does not seem like that big a problem.

If politicians can blame Hungary for their inaction, then this partially protects them from being blamed by voters for not doing anything. But it doesn't protect them at all from being blamed for high fuel prices if they stop importing it from Russia. So they have incentives not to find a solution to this problem.

If you have a 10-adic integer, and you want to reduce it to a 5-adic integer, then to know its last n digits in base 5, you just need to know what it is modulo $5^n$. If you know what it is modulo ${10}^n$, then you can reduce it module $5^n$, so you only need to look at the last n digits in base 10 to find its last n digits in base 5. So a base-10 integer ending in ...93 becomes a base-5 integer ending in ...33, because 93 mod 25 is 18, which, expressed in base 5, is 33.

The Chinese remainder theorem tells us that we can go backwards: given a 5-adic integer and a 2-adic integer, there's exactly one 10-adic integer that reduces to each of them. Let's say we want the 10-adic integer that's 1 in base 5 and -1 in base 2. The last digit is the digit that's 1 mod 5 and 1 mod 2 (i.e. 1). The last 2 digits are the number from 0 to 99 that's 1 mod 25 and 3 mod 4 (i.e. 51). The last 3 digits are the number from 0 to 999 that's 1 mod 125 and 7 mod 8 (i.e. 751). And so on.

(My intuition tells me that if you choose a subset of the primes dividing the base, you can somehow obtain from that a value of $\sqrt{1}$ in a way that maps "none" to 1, and "all" to -1, and the remaining combinations to the irrational integers. No more specific ideas.)

That is correct! In base $p_1^{e_1}\cdot ...\cdot p_n^{e_n}$ (for distinct primes $p_1,...,p_n$), an integer is determined by an integer in each of the bases $p_1,...,p_n$, essentially by the Chinese remainder theorem. In other words, $Q_{p_1^{e_1}\cdot ...\cdot p_n^{e_n}}=Q_{p_1}\times ...\times Q_{p_n}$. In prime base, 1 and -1 are the only two square roots of 1. In arbitrary base, a number squares to 1 iff the number it reduces to in each prime factor of the base also squares to 1, and there's 2 options for each of these factors.