First research proposal for a postdoc application
In mathematics, your situation is very common.  A lot of people don't have any papers written and are still completing their PhD when applying for their first postdoc.  There's nothing "stringent" about "research proposal requirements."  (Are there even any requirements?  Typically, just that something be submitted, I suppose.)  What you'll be evaluated on mostly at your stage is your area of research and letters of recommendation (and possibly your teaching ability, depending on the position).  Yes, people will look at your statement, and you should do a good job at writing it, but don't worry too much about it.

Generally what you should do in a research statement at your stage is:


summarize what you've been working on, and your (partial?) results till now
indicate, in some but not a lot of detail, what are some future things you are interested in working on (these do not need to be things you're definitely going to do)


The point of this statement is:


To see that you can effectively communicate your work/ideas (and possibly to get a sense of how well you understand its context)
To see if what you're doing is of interest to the faculty there
To see that you have some decently thought out ideas for future work