Taking it meta: How would you ensure that if you want to solve hard Q and kept breaking off into easier Q', Q'', Q''', and so on, that eventually your values will remain stable such that you'll still be trying to solve Q? Especially with resource limitations. Or would you even want to? Example: researcher starts out trying to solve P vs. NP. Figures out that she has to solve some problems in information theory first. Likes information theory so much that she forgets about P vs NP and moves on to information theory because she can solve more problems there and hence gain more reputation points and so on.

If we call the above problem R, what will be an easier R'? Is R entirely isomorphic to the problem of stability under self-modification?