Lambda the Ultimate

I've just finished a small article on multimaps which (among other things) defines an interesting recursive definition of numerals. Here is the abstract:

Ordinary maps must contain only single occurrences of their domain values, while multimaps may contain multiple occurrences of both domain and range values.
In this short article we relax the occurrence type to be of any type - if such type obeys some kind of number law. Because of this relaxation and because multimaps behave like numbers, multimaps can be the occurrence type of other multimaps.
We explore this idea with some sketchy code snippets and finish with a recursive multiple of nothing.