> I haven't looked at this in detail, but I would have 
> thought you could have extracted what you needed from 
> the `numbering` part of a Sec, which is just 
> a list of integers, e.g. 2, 4, 2. 
>
> If your top level header is parts, then the first 
> number is the part, the second the chapter, the 
> third the section.  Then it's just a matter of 
> converting the part to a roman numeral when the 
> other numbers are absent, and otherwise ignoring 
> the part and concatenating the other numbers 
> with '.' between... 
>

The problem is that part numbers don’t affect chapter numbers:

   - I. Part 1
      - Chapter 1
      - Chapter 2
   - II. Part 2
      - Chapter 3
      - Chapter 4
   
The first part of my filter numbers Headers properly (to be used with HTML 
and parts):

   - Visit Headers via a filter.
   - Per Header:
      - Update a counter (with one integer per content entity): depending 
      on the level of the Header, while correctly handling part numbers.
      - Prefix the Header’s content with the properly formatted counter.
   
Given that I already track Headers and their numbers:

   - I just additionally keep a mapping from chapter IDs to a list of the 
   chapter’s Headers.
   - For the chapter TOC, I transform this list to nested bullet lists, in 
   a second pass.
   

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