So 'my version' of UDT is perhaps brushing over the distinction between "de facto copies of the agent that were not explicitly labelled as such in the problem statement" and "places where a superbeing or telepathic robot (i.e. Omega) is simulating the agent"?

The former would be subroutines of the world-program different from S but with the same source code as S, whereas the latter would be things of the form "Omega_predict(S, argument)"? (And a 'location of the agent explicitly defined as such' would just be a place where S itself is called?)

That could be quite important...

So I wonder how all this affects decision-making. If you have an alternate version of Newcomb's paradox where rather than OmegaPredict(S) we have OmegaPredict(T) for some T with the same source code as S, does UDT two-box?

Also, how does it square with the idea that part of what it means for an agent to be following UDT is that it has a faculty of 'mathematical intuition' by which it computes the probabilities of possible execution histories (based on the premise that its own output is Y)? Is it unreasonable to suppose that 'mathematical intuition' extends as far as noticing when two programs have the same source code?