Put a half-baked paper in arXiv for the purpose of documentation
ArXiv.org is a preprint server.  It is not intended for your purposes.  

Even though people do upload all kinds of documents (half baked ideas, their PhD thesis, lecture notes, ...), I personally think it inappropriate.

You might consider putting it on your website, or even emailing it to people who are likely to be interested.  Or, make time to finish it!