People often try to solve the problem of counterfactuals by suggesting that there will always be some uncertainty. An AI may know its source code perfectly, but it can’t perfectly know the hardware it is running on.
How could Emmy, an embedded agent, know its source code perfectly, or even be certain that it is a computing device under the Church-Turing definition? Such certainty would seem dogmatic. Without such certainty, the choice of 10 rather than 5 cannot be firmly classified as an error. (The classification as an error seemed to play an important role in your discussion.) So Emmy has a motivation to keep looking and find that U(10)=10.
How could Emmy, an embedded agent, know its source code perfectly, or even be certain that it is a computing device under the Church-Turing definition? Such certainty would seem dogmatic. Without such certainty, the choice of 10 rather than 5 cannot be firmly classified as an error. (The classification as an error seemed to play an important role in your discussion.) So Emmy has a motivation to keep looking and find that U(10)=10.