If they have source code, then they are not perfectly rational and cannot in general implement LDT. They can at best implement a boundedly rational subset of LDT, which will have flaws.
Assume the contrary: Then each agent can verify that the other implements LDT, since perfect knowledge of the other’s source code includes the knowledge that it implements LDT. In particular, each can verify that the other’s code implements a consistent system that includes arithmetic, and can run the other on their own source to consequently verify that they themselves implement a consistent system that includes arithmetic. This is not possible for any consistent system.
The only way that consistency can be preserved is that at least one cannot actually verify that the other has a consistent deduction system including arithmetic. So at least one of those agents is not a LDT agent with perfect knowledge of each other’s source code.
We can in principle assume perfectly rational agents that implement LDT, but they cannot be described by any algorithm and we should be extremely careful in making suppositions about what they can deduce about each other and themselves.
Temporarily adopting this sort of model of “AI capabilities are useful compared to human IQs”:
With IQ 100 AGI (i.e. could do about the same fraction of tasks as well as a sample of IQ 100 humans), progress may well be hyper exponentially fast: but the lead-in to a hyper-exponentially fast function could be very, very slow. The majority of even relatively incompetent humans in technical fields like AI development have greater than IQ 100. Eventually quantity may have a quality of its own, e.g. after there were very large numbers of these sub-par researcher equivalents running at faster than human and coordinated better than I would expect average humans to be.
Absent enormous numerical or speed advantages, I wouldn’t expect substantial changes in research speed until something vaguely equivalent to IQ 160 or so.
Though in practice, I’m not sure that human measures of IQ are usefully applicable to estimating rates of AI-assisted research. They are not human, and only hindsight could tell what capabilities turn out to be the most useful to advancing research. A narrow tool along the lines of AlphaFold could turn out to be radically important to research rate without having anything that you could characterize as IQ. On the other hand, it may turn out that exceeding human research capabilities isn’t practically possible from any system pretrained on material steeped in existing human paradigms and ontology.