## Questions We Still Have:

On integral boxes:

1. We still don't have a closed-form expression for the length of the path from the corner. Perhaps this is not possible.
2. Is it possible to tell if the {$a\times b\times c$} box is generic without repeatedly applying {$\Delta$}?
3. Is there an operation for which the GCD is really the greatest common ... ?
4. Is there an operation for which the LCM is really the least common ... ?
5. For what boxes is there more than one different loop length?
6. How many possible loop lengths can there be on a box?
7. Is there anything one can say about how destinations or loops behave under the {$C$} mapping ([A Generalization of Continued Fractions]])?

On analytic boxes:

1. Do abnormal boxes have loops?
2. Which boxes have paths infinite in both directions?
3. Is there a nice geometric description of the action of {$\Delta$} on the box triangle.
4. What can be said about boxes with one or more negative dimensions?