C.29.1:2 - Problem

A useful change of representation alters which distinctions are visible and which operations are easy. That is also why it can alter an answer.

Agreement on object names or on a few numerical examples does not establish agreement of operations. An update can change the source while leaving a proposed summary unchanged. A summary can combine histories that permit different next steps. A transformed equation can be correct on represented inputs but be applied to other inputs that have no source counterpart. Even an exact change of coordinates can be followed by a lossy projection that no longer answers the original question.

To reuse the result, the practitioner constructs the correspondence, recovers the result’s dependencies, and compares the operations in the direction of use. When exact transfer fails, the same work should reveal whether an added distinction, a smaller domain or a weaker conclusion is sufficient.

The central question is: what can be concluded in the receiving account, and returned to the working question, from the correspondence that has actually been established?