 It is an age-old tradition in foundational investigations to provide a foundation that is not only obviously consistent, but obviously true, and from which all the results in the branch(es) of mathematics being founded will follow logically. Moreover, this following logically is itself something that must be epistemically accessible—hence the importance of checkable proof. A foundational effort can be directed at many different branches of mathematics simultaneously, or just at some particular branch, such as arithmetic. In the former case, it is understandable if the foundational theory chosen (such as ZFC) has a higher consistency strength in relation to any one branch of mathematics being founded. But if the effort is directed at just that one branch (say, arithmetic), then the foundation provided should be of a consistency-strength that is as low as possible, in relation to that branch. 