
Questions We Still Have:
On integral boxes:
 We still don't have a closedform expression for the length of the path from the corner. Perhaps this is not possible.
 Is it possible to tell if the {$a\times b\times c$} box is generic without repeatedly applying {$\Delta$}?
 Is there an operation for which the GCD is really the greatest common ... ?
 Is there an operation for which the LCM is really the least common ... ?
 For what boxes is there more than one different loop length?
 How many possible loop lengths can there be on a box?
 Is there anything one can say about how destinations or loops behave under the {$C$} mapping ([A Generalization of Continued Fractions]])?
On analytic boxes:
 Do abnormal boxes have loops?
 Which boxes have paths infinite in both directions?
 Is there a nice geometric description of the action of {$\Delta$} on the box triangle.
 What can be said about boxes with one or more negative dimensions?
