Another question. HCH is defined as a fixed point of a certain process. But that process probably has many fixed points, some of which might be weird. For example, HCH could return a “universal answer” that brainwashes the human using it into returning the same “universal answer”. Or it could be irrationally convinced that e.g. God exists but a proof of that can’t be communicated. How does the landscape of fixed points look like? Since we’ll presumably approximate HCH by something other than actually simulating a lot of people, will the approximation lead to the right fixed point?
Yes, if the queries aren’t well-founded then HCH isn’t uniquely defined even once you specify H, there is a class of solutions. If there is a bad solution, I think you need to do work to rule it out and wouldn’t count on a method magically finding the answer.