Can my employer require me to document what I know?

I am working on a large, complicated project that several teams have tried to complete in the past, and it was shelved because of the complexity. I have, though a lot of hard work, long hours, and what must be a bizarre form of intellect have figured out how how to do what others have not been able to do. I have not been compensated for this accomplishment above and beyond my regular salary, nor do I really expect to be, even though the work is not what I was hired to do.

In the course of getting the project to work, I learned a lot about our company systems, not from work process but from a logic process. I pretty much had to figure out how things worked in order to my project work. What I know about the systems exists in my head and in thousands of e-mails to my manager and coworkers.

Can the company (not my direct manager or area) require me to document what I know about the systems and how I arrived at the understanding that I have? It would seem to not be in my own best interest to do so, as there are projects coming up that would require my knowledge in order to be successful. A lot of what makes the knowledge different is not so much what I know, but the thought process that I follow to arrive at the conclusions and the way I look at the work we do.

If I document what I know, then I am potentially signing away intellectual capital that I have, which is a leveraging point for a different role and more money. I don’t have a contract with the company. I understand that what I know or do on work time is proprietary to my employer, and how I did my assigned project is documented. What’s not documented is all the extra work, insights, how I figured things out. Can they make me document these things?