up nav for parent of parent

We need to check whether an antora page with an empty parent section and with a non-empty grandparent section which is not the document root, has a correctly functioning Up navigation button. For example consider the following breadcrumb:
```
home, section1, section2, section3
```

If section2 is empty and section1 is non-empty, what is shown in the pagination controls for section3 and what does each button do?